Official Paper

IBPS PO Prelims Memory Based Paper (Held On: 23 August 2025 Shift 1) (Previous Year Paper)

100 questions · 60 minutes · with answers · free

Reasoning Ability (35 questions)

Directions: Read the information and answer the given questions.

Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

The one who likes Yellow showcases immediately before D. E likes neither Red nor Green. A showcases in the month that has an even number of days. A showcases two persons after the one who likes Red. F showcases on an odd-numbered date, but after A. C showcases three persons before the one who showcases immediately after the one who likes Black. C does not showcase on an even-numbered date. A does not like Black. The one who likes Green showcases in the same month as E. Neither C nor B likes Yellow and White.

1

Who among the following person showcases on 16 August?

  1. ((a))

    The one who likes Black

  2. ((b))

    The one who likes Green

  3. ((c))

    A

  4. ((d))

    B

  5. ((e))

    D

Show Answer
Answer: ((e))

D

Given: Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

1. A showcases in the month that has an even number of days. 

Here, we have 2 Cases i.e., Case 1 and Case 2.

MonthsDatesPersons - Color
Case 1Case 2
March (31)9
16
June (30)9A
16A
August (31)9
16

 

2. A showcases two persons after the one who likes Red. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9
16

 

3. F showcases on an odd-numbered date, but after A. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9FF
16

 

4. C showcases three persons before the one who showcases immediately after the one who likes Black.  5. C does not showcase on an even-numbered date. 

Here, we have one more subcase of Case 2.

MonthsDatesPersons - Color
Case 1Case 2Case 2a
March (31)9C - RedC -
16- Red- Red
June (30)9A - Black- BlackC -
16AA
August (31)9FFF - Black
16

 

6. A does not like Black. 

Now, we can eliminate Case 1.

MonthsDatesPersons - Color
Case 2Case 2a
March (31)9C -
16- Red- Red
June (30)9- BlackC -
16AA
August (31)9FF - Black
16

 

7. The one who likes Green showcases in the same month as E.  8. E likes neither Red nor Green. 

Now, we can eliminate Case 2a, but we have a new subcase of Case 2.

MonthsDatesPersons - Color
Case 2Case 2(i)
March (31)9C -C -
16- Red- Red
June (30)9E - Black- Black
16A - GreenA
August (31)9FF - Green
16E -

 

  1. The one who likes Yellow showcases immediately before D.
  2. Neither C nor B likes Yellow and White.

Now, we can eliminate Case 2(i).

MonthsDatesPersons - Color
Case 2
March (31)9C -
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

This is our final arrangement,

MonthsDatesPersons - Color
Case 2
March (31)9C - Blue
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

Hence, the correct answer is D.

2

On which of the following month and date does F showcase?

  1. ((a))

    9 August

  2. ((b))

    9 March

  3. ((c))

    9 June

  4. ((d))

    16 June

  5. ((e))

    16 August

Show Answer
Answer: ((a))

9 August

Given: Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

1. A showcases in the month that has an even number of days. 

Here, we have 2 Cases i.e., Case 1 and Case 2.

MonthsDatesPersons - Color
Case 1Case 2
March (31)9
16
June (30)9A
16A
August (31)9
16

 

2. A showcases two persons after the one who likes Red. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9
16

 

3. F showcases on an odd-numbered date, but after A. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9FF
16

 

4. C showcases three persons before the one who showcases immediately after the one who likes Black.  5. C does not showcase on an even-numbered date. 

Here, we have one more subcase of Case 2.

MonthsDatesPersons - Color
Case 1Case 2Case 2a
March (31)9C - RedC -
16- Red- Red
June (30)9A - Black- BlackC -
16AA
August (31)9FFF - Black
16

 

6. A does not like Black. 

Now, we can eliminate Case 1.

MonthsDatesPersons - Color
Case 2Case 2a
March (31)9C -
16- Red- Red
June (30)9- BlackC -
16AA
August (31)9FF - Black
16

 

7. The one who likes Green showcases in the same month as E.  8. E likes neither Red nor Green. 

Now, we can eliminate Case 2a, but we have a new subcase of Case 2.

MonthsDatesPersons - Color
Case 2Case 2(i)
March (31)9C -C -
16- Red- Red
June (30)9E - Black- Black
16A - GreenA
August (31)9FF - Green
16E -

 

  1. The one who likes Yellow showcases immediately before D.
  2. Neither C nor B likes Yellow and White.

Now, we can eliminate Case 2(i).

MonthsDatesPersons - Color
Case 2
March (31)9C -
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

This is our final arrangement,

MonthsDatesPersons - Color
Case 2
March (31)9C - Blue
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

Hence, the correct answer is 9 August.

3

Which of the following colors does D like?

  1. ((a))

    Green

  2. ((b))

    Yellow

  3. ((c))

    White

  4. ((d))

    Blue

  5. ((e))

    Red

Show Answer
Answer: ((c))

White

Given: Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

1. A showcases in the month that has an even number of days. 

Here, we have 2 Cases i.e., Case 1 and Case 2.

MonthsDatesPersons - Color
Case 1Case 2
March (31)9
16
June (30)9A
16A
August (31)9
16

 

2. A showcases two persons after the one who likes Red. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9
16

 

3. F showcases on an odd-numbered date, but after A. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9FF
16

 

4. C showcases three persons before the one who showcases immediately after the one who likes Black.  5. C does not showcase on an even-numbered date. 

Here, we have one more subcase of Case 2.

MonthsDatesPersons - Color
Case 1Case 2Case 2a
March (31)9C - RedC -
16- Red- Red
June (30)9A - Black- BlackC -
16AA
August (31)9FFF - Black
16

 

6. A does not like Black. 

Now, we can eliminate Case 1.

MonthsDatesPersons - Color
Case 2Case 2a
March (31)9C -
16- Red- Red
June (30)9- BlackC -
16AA
August (31)9FF - Black
16

 

7. The one who likes Green showcases in the same month as E.  8. E likes neither Red nor Green. 

Now, we can eliminate Case 2a, but we have a new subcase of Case 2.

MonthsDatesPersons - Color
Case 2Case 2(i)
March (31)9C -C -
16- Red- Red
June (30)9E - Black- Black
16A - GreenA
August (31)9FF - Green
16E -

 

  1. The one who likes Yellow showcases immediately before D.
  2. Neither C nor B likes Yellow and White.

Now, we can eliminate Case 2(i).

MonthsDatesPersons - Color
Case 2
March (31)9C -
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

This is our final arrangement,

MonthsDatesPersons - Color
Case 2
March (31)9C - Blue
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

Hence, the correct answer is White.

4

How many persons showcase before C?

  1. ((a))

    None

  2. ((b))

    One

  3. ((c))

    Two

  4. ((d))

    Three

  5. ((e))

    Four

Show Answer
Answer: ((a))

None

Given: Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

1. A showcases in the month that has an even number of days. 

Here, we have 2 Cases i.e., Case 1 and Case 2.

MonthsDatesPersons - Color
Case 1Case 2
March (31)9
16
June (30)9A
16A
August (31)9
16

 

2. A showcases two persons after the one who likes Red. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9
16

 

3. F showcases on an odd-numbered date, but after A. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9FF
16

 

4. C showcases three persons before the one who showcases immediately after the one who likes Black.  5. C does not showcase on an even-numbered date. 

Here, we have one more subcase of Case 2.

MonthsDatesPersons - Color
Case 1Case 2Case 2a
March (31)9C - RedC -
16- Red- Red
June (30)9A - Black- BlackC -
16AA
August (31)9FFF - Black
16

 

6. A does not like Black. 

Now, we can eliminate Case 1.

MonthsDatesPersons - Color
Case 2Case 2a
March (31)9C -
16- Red- Red
June (30)9- BlackC -
16AA
August (31)9FF - Black
16

 

7. The one who likes Green showcases in the same month as E.  8. E likes neither Red nor Green. 

Now, we can eliminate Case 2a, but we have a new subcase of Case 2.

MonthsDatesPersons - Color
Case 2Case 2(i)
March (31)9C -C -
16- Red- Red
June (30)9E - Black- Black
16A - GreenA
August (31)9FF - Green
16E -

 

  1. The one who likes Yellow showcases immediately before D.
  2. Neither C nor B likes Yellow and White.

Now, we can eliminate Case 2(i).

MonthsDatesPersons - Color
Case 2
March (31)9C -
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

This is our final arrangement,

MonthsDatesPersons - Color
Case 2
March (31)9C - Blue
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

Hence, the correct answer is None.

5

Four of the following are alike in a certain way. Who among the following does not belong to the group?

  1. ((a))

    D

  2. ((b))

    The one who likes Red

  3. ((c))

    A

  4. ((d))

    E

  5. ((e))

    The one who likes Green

Show Answer
Answer: ((d))

E

Given: Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.

  1. A showcases in the month that has an even number of days. 

Here, we have 2 Cases i.e., Case 1 and Case 2.

MonthsDatesPersons - Color
Case 1Case 2
March (31)9
16
June (30)9A
16A
August (31)9
16

 

  1. A showcases two persons after the one who likes Red. 
MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9
16

 

3. F showcases on an odd-numbered date, but after A. 

MonthsDatesPersons - Color
Case 1Case 2
March (31)9- Red
16- Red
June (30)9A
16A
August (31)9FF
16

 

4. C showcases three persons before the one who showcases immediately after the one who likes Black.  5. C does not showcase on an even-numbered date. 

Here, we have one more subcase of Case 2.

MonthsDatesPersons - Color
Case 1Case 2Case 2a
March (31)9C - RedC -
16- Red- Red
June (30)9A - Black- BlackC -
16AA
August (31)9FFF - Black
16

 

6. A does not like Black. 

Now, we can eliminate Case 1.

MonthsDatesPersons - Color
Case 2Case 2a
March (31)9C -
16- Red- Red
June (30)9- BlackC -
16AA
August (31)9FF - Black
16

 

7. The one who likes Green showcases in the same month as E.  8. E likes neither Red nor Green. 

Now, we can eliminate Case 2a, but we have a new subcase of Case 2.

MonthsDatesPersons - Color
Case 2Case 2(i)
March (31)9C -C -
16- Red- Red
June (30)9E - Black- Black
16A - GreenA
August (31)9FF - Green
16E -

 

  1. The one who likes Yellow showcases immediately before D.
  2. Neither C nor B likes Yellow and White.

Now, we can eliminate Case 2(i).

MonthsDatesPersons - Color
Case 2
March (31)9C -
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

This is our final arrangement,

MonthsDatesPersons - Color
Case 2
March (31)9C - Blue
16B - Red
June (30)9E - Black
16A - Green
August (31)9F - Yellow
16D - White

 

Except for E, all others showcase on even dates.

Hence, the correct answer is E.

6

How many pairs of digits in the number 613955 have as many numbers between them as in the series of natural numbers both in backward and forward directions?

  1. ((a))

    One

  2. ((b))

    Two

  3. ((c))

    Three

  4. ((d))

    Four

  5. ((e))

    Five

Show Answer
Answer: ((c))

Three

Given number: 613955

Forward: (6, 9), (3, 5), (1, 5)

Hence, we can see that 3 such pairs are there.

Directions: Read the information and answer the given questions.

Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

There are exactly two people born between U and W. W is older than 20 years of age. Both P and V are younger than 45 years. Q is not the youngest among the group. The age of R is at most 20 years less than S’s age. There is exactly one person born between U and Q. V was born in the year immediately before P. Q’s age is a perfect cube. The age difference between T and S is at most 10 years, with S being younger.

7

Which of the following combination is correct?

  1. ((a))

    P - 19 years

  2. ((b))

    Q - 28 years

  3. ((c))

    R - 27 years

  4. ((d))

    T - 49 years

  5. ((e))

    U - 59 years

Show Answer
Answer: ((d))

T - 49 years

Given: Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

1. Q’s age is a perfect cube.  2. Q is not the youngest among the group. 

YearsAge (in years)Persons
196659
197649
198243
198936
199728
199827Q
200619
201213

 

3. There is exactly one person born between U and Q. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

YearsAge (in years)Persons
Case 1Case 2
196659
197649
198243
198936U
199728
199827QQ
200619
201213U

 

  1. There are exactly two people born between U and W. 
YearsAge (in years)Persons
Case 1Case 2
196659W/
197649
198243
198936U
199728W
199827QQ
200619W/
201213U

 

  1. W is older than 20 years of age.
YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243
198936U
199728W
199827QQ
200619
201213U

 

6. V was born in the year immediately before P.  7. Both P and V are younger than 45 years. 

YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243V
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age difference between T and S is at most 10 years, with S being younger.
YearsAge (in years)Persons
Case 1Case 2
196659TW
197649ST
198243VS
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age of R is at most 20 years less than S’s age. 

Now, we can eliminate Case 1.

YearsAge (in years)Persons
Case 2
196659W
197649T
198243S
198936U
199728R
199827Q
200619V
201213P

 

Hence, the correct answer is T - 49 years.

8

Which one is odd?

  1. ((a))

    W

  2. ((b))

    T

  3. ((c))

    S

  4. ((d))

    R

  5. ((e))

    Q

Show Answer
Answer: ((d))

R

Given: Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

1. Q’s age is a perfect cube.  2. Q is not the youngest among the group. 

YearsAge (in years)Persons
196659
197649
198243
198936
199728
199827Q
200619
201213

 

3. There is exactly one person born between U and Q. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

YearsAge (in years)Persons
Case 1Case 2
196659
197649
198243
198936U
199728
199827QQ
200619
201213U

 

  1. There are exactly two people born between U and W. 
YearsAge (in years)Persons
Case 1Case 2
196659W/
197649
198243
198936U
199728W
199827QQ
200619W/
201213U

 

  1. W is older than 20 years of age.
YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243
198936U
199728W
199827QQ
200619
201213U

 

6. V was born in the year immediately before P.  7. Both P and V are younger than 45 years. 

YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243V
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age difference between T and S is at most 10 years, with S being younger.
YearsAge (in years)Persons
Case 1Case 2
196659TW
197649ST
198243VS
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age of R is at most 20 years less than S’s age. 

Now, we can eliminate Case 1.

YearsAge (in years)Persons
Case 2
196659W
197649T
198243S
198936U
199728R
199827Q
200619V
201213P

 

Except for R, all others have odd ages.

Hence, the correct answer is R.

9

How many people born between T and U?

  1. ((a))

    None

  2. ((b))

    One

  3. ((c))

    Two

  4. ((d))

    Three

  5. ((e))

    Four

Show Answer
Answer: ((b))

One

Given: Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

1. Q’s age is a perfect cube.  2. Q is not the youngest among the group. 

YearsAge (in years)Persons
196659
197649
198243
198936
199728
199827Q
200619
201213

 

3. There is exactly one person born between U and Q. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

YearsAge (in years)Persons
Case 1Case 2
196659
197649
198243
198936U
199728
199827QQ
200619
201213U

 

  1. There are exactly two people born between U and W. 
YearsAge (in years)Persons
Case 1Case 2
196659W/
197649
198243
198936U
199728W
199827QQ
200619W/
201213U

 

  1. W is older than 20 years of age.
YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243
198936U
199728W
199827QQ
200619
201213U

 

6. V was born in the year immediately before P.  7. Both P and V are younger than 45 years. 

YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243V
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age difference between T and S is at most 10 years, with S being younger.
YearsAge (in years)Persons
Case 1Case 2
196659TW
197649ST
198243VS
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age of R is at most 20 years less than S’s age. 

Now, we can eliminate Case 1.

YearsAge (in years)Persons
Case 2
196659W
197649T
198243S
198936U
199728R
199827Q
200619V
201213P

 

Hence, the correct answer is One.

10

What is the sum of the ages of P and T?

  1. ((a))

    80 years

  2. ((b))

    62 years

  3. ((c))

    90 years

  4. ((d))

    95 years

  5. ((e))

    100 years

Show Answer
Answer: ((b))

62 years

Given: Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

1. Q’s age is a perfect cube.  2. Q is not the youngest among the group. 

YearsAge (in years)Persons
196659
197649
198243
198936
199728
199827Q
200619
201213

 

3. There is exactly one person born between U and Q. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

YearsAge (in years)Persons
Case 1Case 2
196659
197649
198243
198936U
199728
199827QQ
200619
201213U

 

  1. There are exactly two people born between U and W. 
YearsAge (in years)Persons
Case 1Case 2
196659W/
197649
198243
198936U
199728W
199827QQ
200619W/
201213U

 

  1. W is older than 20 years of age.
YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243
198936U
199728W
199827QQ
200619
201213U

 

6. V was born in the year immediately before P.  7. Both P and V are younger than 45 years. 

YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243V
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age difference between T and S is at most 10 years, with S being younger.
YearsAge (in years)Persons
Case 1Case 2
196659TW
197649ST
198243VS
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age of R is at most 20 years less than S’s age. 

Now, we can eliminate Case 1.

YearsAge (in years)Persons
Case 2
196659W
197649T
198243S
198936U
199728R
199827Q
200619V
201213P

 

The sum is = 49 + 13 = 62 years.

Hence, the correct answer is 62 years.

11

Who among the following is the oldest person?

  1. ((a))

    P

  2. ((b))

    Q

  3. ((c))

    W

  4. ((d))

    S

  5. ((e))

    T

Show Answer
Answer: ((c))

W

Given: Eight individuals, namely, P, Q, R, S, T, U, V, and W, were born in different years: 1966, 1976, 1982, 1989, 1997, 1998, 2006, and 2012, but not necessarily in the same order. Their ages are calculated with respect to the year 2025.

  1. Q’s age is a perfect cube.  2. Q is not the youngest among the group. 
YearsAge (in years)Persons
196659
197649
198243
198936
199728
199827Q
200619
201213

 

3. There is exactly one person born between U and Q. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

YearsAge (in years)Persons
Case 1Case 2
196659
197649
198243
198936U
199728
199827QQ
200619
201213U

 

  1. There are exactly two people born between U and W. 
YearsAge (in years)Persons
Case 1Case 2
196659W/
197649
198243
198936U
199728W
199827QQ
200619W/
201213U

 

  1. W is older than 20 years of age.
YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243
198936U
199728W
199827QQ
200619
201213U

 

6. V was born in the year immediately before P.  7. Both P and V are younger than 45 years. 

YearsAge (in years)Persons
Case 1Case 2
196659W
197649
198243V
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age difference between T and S is at most 10 years, with S being younger.
YearsAge (in years)Persons
Case 1Case 2
196659TW
197649ST
198243VS
198936PU
199728W
199827QQ
200619V
201213UP

 

  1. The age of R is at most 20 years less than S’s age. 

Now, we can eliminate Case 1.

YearsAge (in years)Persons
Case 2
196659W
197649T
198243S
198936U
199728R
199827Q
200619V
201213P

 

Hence, the correct answer is W.

12

In the question below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

I. Some bacteria are virus

II. No virus is malaria

III. Only a few mosquito are bacteria

Conclusions:

I. No malaria is bacteria

II. Some virus is malaria

III. Some mosquito are not bacteria

  1. ((a))

    Only conclusion I follows

  2. ((b))

    Only conclusion III follows

  3. ((c))

    Both conclusion II and III follows

  4. ((d))

    Only conclusion II follows

  5. ((e))

    All the conclusion follows

Show Answer
Answer: ((b))

Only conclusion III follows

The least possible Venn diagram for the given statements is as follows,

I. No malaria is bacteria → False (It can be possible but it is not definite)

II. Some virus is malaria → False (It is definitely false)

III. Some mosquito are not bacteria → True (It is definite)

Only conclusion III follows.

13

In the question below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

I. No verb is article

II. Only a few nouns are verb

III. Some articles are not preposition

Conclusions:

I. Some prepositions are verbs

II. All verb is noun

III. Some article is noun

  1. ((a))

    None of the conclusion follows

  2. ((b))

    Only conclusion II follows

  3. ((c))

    Both conclusion I and II follows

  4. ((d))

    All the conclusion follows

  5. ((e))

    Only conclusion I follows

Show Answer
Answer: ((a))

None of the conclusion follows

The least possible Venn diagram for the given statements is as follows,

I. Some prepositions are verbs → False (It can be possible but it is not definite)

II. All verb is noun → False (It can be possible but it is not definite)

III. Some article is noun → False (It can be possible but it is not definite)

Hence, none of the conclusion follows.

14

In the question below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

I. All Men are Good

II. Some Boys are Bad

III. Few Bad is Good

Conclusions:

I. Some boys are not bad

II. Some men are good

III. Some bad are not good

  1. ((a))

    Only conclusion I follows

  2. ((b))

    Only conclusion II follows

  3. ((c))

    Both conclusion I and III follow

  4. ((d))

    Both conclusion II and III follow

  5. ((e))

    None of the conclusion follows

Show Answer
Answer: ((b))

Only conclusion II follows

Concept 1:

  • Meaning of "Some A are B" in Syllogism - there is at least one point in A which is in B.
  • Meaning of "All A are B" in Syllogism - each point of A is in B.
  • This explains why "some" can be considered as a subset of "all".
  • Therefore, if "All A are B" is true, then "some A are B" is always true.

Keywords:

  1. All and some not
  2. Some and no

Conditions:

  1. The same elements are used in the two conclusions. For example, in this case, the elements jungles and malls are common to both conclusions.
  2. Both conclusions should be possibilities. That is, they should be false because the conclusion is possible but not definite.

Then, the pair of conclusions are considered as complementary pairs.

Concept 2: Few, Only a few, Only.

a) Only a few - means only "some" not "all".

Example1-

1. Only a few A are B implies that-

  • Some A are B
  • All A are B is a possibility is false because Only a few A are B. All A cannot be B

"But"

  • all B can be A.

b) "Few" is same as "some".

Example2-

  1. few A are B implies that-
  • Some A are B
  • All A are B is a possibility
  • Some B are A.
  • Some A are not B is a possibility.

3) Concept of Only:

c) Only "A is B" is the same as "all B are A".

Examples

  • Only A are B.
  • Some A are B.

The least possible Venn diagram for the given statements is as follows,

Explanation:

I. Some Boys are not Bad → False (As some Boys are Bad, and remaining part of Boys and Bad whether it is true or not. So, it is false)

II. Some Men are Good → True (As All Men are Good → some Men are Good. So, it is true) 

III. Some Bad are not Good → False (it is possible but not definite. So, it is false)

Conclusion

"Only conclusion II follows" is the correct answer.

Direction: Read the following information carefully and answer the questions based on given information.

A certain number of persons sit on the horizontal row and faces towards North direction. Only three persons sit between S and W. Only two persons sit between X and R. M sits at the extreme end. H sits second to the left of X. E sits exactly at middle of S and W. R sits two places away from M. E sits immediate right to H. W sits to the right of X. F sits to the right of X. The number of persons sit to the left of S is same as to that of to the right of F. Y and W sit immediate next to each other.

15

Who among the following person sits immediate left to S?

  1. ((a))

    X

  2. ((b))

    H

  3. ((c))

    Y

  4. ((d))

    R

  5. ((e))

    None 

Show Answer
Answer: ((e))

None 

  1. M sits at the extreme end.

  2. R sits two places away from M.

  3. Only two persons sit between X and R.

  1. H sits second to the left of X.

  2. E sits immediate right to H.

  1. E sits exactly at middle of S and W.

  2. Only three persons S and W. Therefore, case 1 is eliminated.

  3. W sits to the right of X.

  1. The number of persons sit to the left of S is same as to that of to the right of F.

  2. F sits to the right of X.

  3. Y and W sit immediate next to each other. Hence, the final arrangement is as follows

Hence, no one sits to the left of S.

16

What is position of Y with respect to H?

  1. ((a))

    Third to the right

  2. ((b))

    Fifth to the left

  3. ((c))

    Second to the right

  4. ((d))

    Fourth to the right 

  5. ((e))

    Fourth to the left

Show Answer
Answer: ((d))

Fourth to the right 

  1. M sits at the extreme end.

  2. R sits two places away from M.

  3. Only two persons sit between X and R.

  1. H sits second to the left of X.

  2. E sits immediate right to H.

  1. E sits exactly at middle of S and W.

  2. Only three persons S and W. Therefore, case 1 is eliminated.

  3. W sits to the right of X.

  1. The number of persons sit to the left of S is same as to that of to the right of F.

  2. F sits to the right of X.

  3. Y and W sit immediate next to each other. Hence, the final arrangement is as follows

Hence, Y sits fourth to the left of H.

17

Which of the following statement is/are correct?

A) X sits second to the left of Y.

B) H sits third to the right of S.

C) R sits second to the right of M.

  1. ((a))

    Only A

  2. ((b))

    Both A and C

  3. ((c))

    Only C

  4. ((d))

    Only B

  5. ((e))

    Both 1 and 4

Show Answer
Answer: ((a))

Only A

  1. M sits at the extreme end.

  2. R sits two places away from M.

  3. Only two persons sit between X and R.

  1. H sits second to the left of X.

  2. E sits immediate right to H.

  1. E sits exactly at middle of S and W.

  2. Only three persons S and W. Therefore, case 1 is eliminated.

  3. W sits to the right of X.

  1. The number of persons sit to the left of S is same as to that of to the right of F.

  2. F sits to the right of X.

  3. Y and W sit immediate next to each other. Hence, the final arrangement is as follows

Since, X sits second to the left of Y. Therefore, statement A is correct.

H sits immediate to S. Therefore, statement B is incorrect.

R sits second to the left of M. Therefore, statement C is incorrect.

Hence, the correct answer is option 1.

18

If it is possible to make only one meaningful English word with the first, the second, the fifth and the sixth letters of the word EDUCATION, which of the following will be the third letter of that word from the left end? If no such word can be made give ‘X’ as the answer and if more than one such word can be made give ‘Y’ as the answer.

  1. ((a))

    T

  2. ((b))

    Y

  3. ((c))

    X

  4. ((d))

    E

  5. ((e))

    A

Show Answer
Answer: ((a))

T

Word: EDUCATION

1st letter = E; 2nd letter = D; 5th letter = A; 6th letter = T

Letters given: EDAT.

Possible words: DATE.

Hence, only 1 such word is possible.

Clearly, the third letter of the possible word from the left end is T.

Direction: Read the following information carefully and answer the questions based on given information.

Six boxes J, L, N, Q, R and V placed one over another and contain six different colours which are Blue, Green, Pink, Red, White and Yellow but not necessarily in same order. Box L placed four boxes above the box which contains Pink colour. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Box V placed just above the box which contains Red colour. As many boxes placed above the box contains Green colour as many below the box J. The box contains Red colour and the box contains Pink colour placed adjacent to each other. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Neither V nor R likes Green or White colour. The box contains Blue colour is placed below the box that contains Yellow colour.

19

Which of the following box is placed just above the box that contains Yellow colour?

  1. ((a))

    L

  2. ((b))

    Q

  3. ((c))

    The box that contains Green colour.

  4. ((d))

    The box that contains White colour.

  5. ((e))

    More than one option.

Show Answer
Answer: ((e))

More than one option.

Here, boxes are J, L, N, Q, R and V and colours are Blue, Green, Pink, Red, White and Yellow.

  1. Box L placed four boxes above the box which contains Pink colour.

  2. The box contains Red colour and the box contains Pink colour placed adjacent to each other.  3) Box V placed just above the box which contains Red colour.

Case – 1Box – 2Case – 3
BoxesColoursBoxesColoursBoxesColours
LL
L
V
VRed
RedPinkVPink
PinkRed

 

  1. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Therefore, case 3 is eliminated.

  2. As many boxes placed above the box contains Green colour as many below the box J. 

Case – 1(a)Case – 1(b)Case – 2(a)Case – 2(b)
BoxesColoursBoxesColoursBoxesColoursBoxesColours
GreenLGreenL
LWhiteLWhiteWhiteWhite
JVVGreen
VVGreenRedJRed
NRedNRedNPinkNPink
JPinkPinkJ

 

  1. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Therefore, case 1(a) is eliminated.

  2. Neither V nor R likes Green or White colour. Therefore, case 1(b) and case 2(b) are eliminated.

  3. The box contains Blue colour is placed below the box that contains Yellow colour. Hence, the final arrangement is as follow

BoxesColours
LGreen
QWhite
VYellow
RRed
NPink
JBlue

 

Since, Box Q which contains White colour placed just above the box that contains Yellow colour.

Hence, the correct answer is more than one option.

20

How many boxes are placed between the Box L and the box R?

  1. ((a))

    As many boxes placed below the box J.

  2. ((b))

    As many boxes placed above the box Q.

  3. ((c))

    As many boxes placed below the box that contains Red colour.

  4. ((d))

    As many boxes placed between the Box V and the Box N.

  5. ((e))

    None of these.

Show Answer
Answer: ((c))

As many boxes placed below the box that contains Red colour.

Here, boxes are J, L, N, Q, R and V and colours are Blue, Green, Pink, Red, White and Yellow.

  1. Box L placed four boxes above the box which contains Pink colour.

  2. The box contains Red colour and the box contains Pink colour placed adjacent to each other.  3) Box V placed just above the box which contains Red colour.

Case – 1Box – 2Case – 3
BoxesColoursBoxesColoursBoxesColours
LL
L
V
VRed
RedPinkVPink
PinkRed

 

  1. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Therefore, case 3 is eliminated.

  2. As many boxes placed above the box contains Green colour as many below the box J. 

Case – 1(a)Case – 1(b)Case – 2(a)Case – 2(b)
BoxesColoursBoxesColoursBoxesColoursBoxesColours
GreenLGreenL
LWhiteLWhiteWhiteWhite
JVVGreen
VVGreenRedJRed
NRedNRedNPinkNPink
JPinkPinkJ

 

  1. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Therefore, case 1(a) is eliminated.

  2. Neither V nor R likes Green or White colour. Therefore, case 1(b) and case 2(b) are eliminated.

  3. The box contains Blue colour is placed below the box that contains Yellow colour. Hence, the final arrangement is as follow

BoxesColours
LGreen
QWhite
VYellow
RRed
NPink
JBlue

 

Since, two boxes placed between the Box L and the Box R and same number of boxes placed below the box that contains Red colour which is Box R.

Hence, the correct answer is As many boxes placed below the box that contains Red colour.

21

Which of the following combination is incorrect?

  1. ((a))

    L - Green

  2. ((b))

    Q - White

  3. ((c))

    R - Red

  4. ((d))

    N - Yellow

  5. ((e))

    J - Blue

Show Answer
Answer: ((d))

N - Yellow

Here, boxes are J, L, N, Q, R and V and colours are Blue, Green, Pink, Red, White and Yellow.

  1. Box L placed four boxes above the box which contains Pink colour.

  2. The box contains Red colour and the box contains Pink colour placed adjacent to each other.  3) Box V placed just above the box which contains Red colour.

Case – 1Box – 2Case – 3
BoxesColoursBoxesColoursBoxesColours
LL
L
V
VRed
RedPinkVPink
PinkRed

 

  1. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Therefore, case 3 is eliminated.

  2. As many boxes placed above the box contains Green colour as many below the box J. 

Case – 1(a)Case – 1(b)Case – 2(a)Case – 2(b)
BoxesColoursBoxesColoursBoxesColoursBoxesColours
GreenLGreenL
LWhiteLWhiteWhiteWhite
JVVGreen
VVGreenRedJRed
NRedNRedNPinkNPink
JPinkPinkJ

 

  1. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Therefore, case 1(a) is eliminated.

  2. Neither V nor R likes Green or White colour. Therefore, case 1(b) and case 2(b) are eliminated.

  3. The box contains Blue colour is placed below the box that contains Yellow colour. Hence, the final arrangement is as follow

BoxesColours
LGreen
QWhite
VYellow
RRed
NPink
JBlue

 

Hence, the incorrect combination N - Yellow.

22

Which of the following statement(s) is/are correct?

  1. ((a))

    The Box R contains Pink colour.

  2. ((b))

    Only two boxes are placed between the Box V and Box R.

  3. ((c))

    Only one box is placed below the box that contains Blue colour.

  4. ((d))

    Box J contains Blue colour.

  5. ((e))

    None of these.

Show Answer
Answer: ((d))

Box J contains Blue colour.

Here, boxes are J, L, N, Q, R and V and colours are Blue, Green, Pink, Red, White and Yellow.

  1. Box L placed four boxes above the box which contains Pink colour.

  2. The box contains Red colour and the box contains Pink colour placed adjacent to each other.  3) Box V placed just above the box which contains Red colour.

Case – 1Box – 2Case – 3
BoxesColoursBoxesColoursBoxesColours
LL
L
V
VRed
RedPinkVPink
PinkRed

 

  1. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Therefore, case 3 is eliminated.

  2. As many boxes placed above the box contains Green colour as many below the box J. 

Case – 1(a)Case – 1(b)Case – 2(a)Case – 2(b)
BoxesColoursBoxesColoursBoxesColoursBoxesColours
GreenLGreenL
LWhiteLWhiteWhiteWhite
JVVGreen
VVGreenRedJRed
NRedNRedNPinkNPink
JPinkPinkJ

 

  1. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Therefore, case 1(a) is eliminated.

  2. Neither V nor R likes Green or White colour. Therefore, case 1(b) and case 2(b) are eliminated.

  3. The box contains Blue colour is placed below the box that contains Yellow colour. Hence, the final arrangement is as follow

BoxesColours
LGreen
QWhite
VYellow
RRed
NPink
JBlue

 

Since, the Box R contains Red colour. Therefore, statement first is incorrect.

Box V and Box R are placed adjacent to each other. Therefore, statement second is incorrect.

The box contains Blue colour placed at bottom position. Therefore, statement third is incorrect.

Box J contains Blue colour. Therefore, statement fourth is correct.

Hence, the correct statement is Box J contains Blue colour.

23

Which of the following box is placed two boxes above the box that contains Blue colour?

  1. ((a))

    The box that contains White colour.

  2. ((b))

    Box V

  3. ((c))

    The box that is placed just below the box that contains Yellow colour.

  4. ((d))

    Box Q

  5. ((e))

    The box that contains Pink colour.

Show Answer
Answer: ((c))

The box that is placed just below the box that contains Yellow colour.

Here, boxes are J, L, N, Q, R and V and colours are Blue, Green, Pink, Red, White and Yellow.

  1. Box L placed four boxes above the box which contains Pink colour.

  2. The box contains Red colour and the box contains Pink colour placed adjacent to each other.

  3. Box V placed just above the box which contains Red colour.

Case – 1Box – 2Case – 3
BoxesColoursBoxesColoursBoxesColours
LL
L
V
VRed
RedPinkVPink
PinkRed

 

  1. Only two boxes are placed between the box contains White colour and Box N, neither of them placed at top or bottom positions. Therefore, case 3 is eliminated.

  2. As many boxes placed above the box contains Green colour as many below the box J. 

Case – 1(a)Case – 1(b)Case – 2(a)Case – 2(b)
BoxesColoursBoxesColoursBoxesColoursBoxesColours
GreenLGreenL
LWhiteLWhiteWhiteWhite
JVVGreen
VVGreenRedJRed
NRedNRedNPinkNPink
JPinkPinkJ

 

  1. Box Q placed below the Box L but likes neither Yellow nor Blue colour. Therefore, case 1(a) is eliminated.

  2. Neither V nor R likes Green or White colour. Therefore, case 1(b) and case 2(b) are eliminated.

  3. The box contains Blue colour is placed below the box that contains Yellow colour. Hence, the final arrangement is as follow

BoxesColours
LGreen
QWhite
VYellow
RRed
NPink
JBlue

 

Since, the Box R which contains Red colour and placed just below the Box V which contains Yellow colour is placed two boxes above the box J which contains Blue colour.

Hence, the correct answer is The box that is placed just below the box that contains Yellow colour.

24

Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statements:

A = D < C < B ≤ G > E; S < Q = E

Conclusions

I. A ≤ G

II. C > S

  1. ((a))

    Only II is True

  2. ((b))

    Only I is True

  3. ((c))

    Both I and II are True

  4. ((d))

    Either I or II is True

  5. ((e))

    None is true

Show Answer
Answer: ((e))

None is true

Given statements: A = D < C < B ≤ G > E; S < Q = E

On combining: A = D < C < B ≤ G > E = Q > S

Conclusions:

I. A ≤ G → False (as A = D < C < B ≤ G → A < G)

II. C > S → False (as C < B ≤ G > E = Q > S → clear relation between C and S cannot be determined)

Hence, none is true.

25

Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statements: B = F ≤ J < V ≤ W; B < U > P

Conclusions

I. B < W

II. U > F

  1. ((a))

    Only II is True

  2. ((b))

    Only I is True

  3. ((c))

    Both I and II are True

  4. ((d))

    Either I or II is True

  5. ((e))

    None is true

Show Answer
Answer: ((c))

Both I and II are True

Given statements: B = F ≤ J < V ≤ W; B < U > P

On combining: P < U > B = F ≤ J < V ≤ W

Conclusions:

I. B < W → True (as B = F ≤ J < V ≤ W → B < W)

II. U > F → True (as U > B = F → U > F)

Hence, Both I and II are True.

26

Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statements: R ≥ U = X, K ≤ W = S < A > R

Conclusions:

I. A > X

II. W < U

  1. ((a))

    Only II is True

  2. ((b))

    Only I is True

  3. ((c))

    Both I and II are True

  4. ((d))

    Either I or II is True

  5. ((e))

    None is true

Show Answer
Answer: ((b))

Only I is True

Given statements: R ≥ U = X, K ≤ W = S < A > R

On combining: K ≤ W = S < A > R ≥ U = X

Conclusions:

I. A > X → True (as K ≤ W = S < A > R ≥ U = X → A > X)

II. W < U → False (as K ≤ W = S < A > R ≥ U = X → clear relation between W and U cannot be determined)

Hence, Only I is True.

Directions: Read the information and answer the given questions.

Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

J is the neighbour of the person who faces the one seated second to the left of T.  I sits second to the left of N.  R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. M sits diagonally opposite to P, who sits third to the right of S. The one who sits second to the left of Q sits opposite to M. Q is seated three places away from U, who occupies one of the extreme ends. T sits to the right of S but is not an immediate neighbor of Q. S is seated opposite the person who is immediately to the right of K. L and P are not seated directly opposite to each other, and also don't sit at the ends. M and P do not sit at the ends.

27

Which one is odd?

  1. ((a))

    N

  2. ((b))

    U

  3. ((c))

    Q

  4. ((d))

    H

  5. ((e))

    T

Show Answer
Answer: ((c))

Q

Given: Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

1. Q is seated three places away from U, who occupies one of the extreme ends. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

  1. The one who sits second to the left of Q sits opposite to M.

  1. M sits diagonally opposite to P, who sits third to the right of S.

  1. T sits to the right of S but is not an immediate neighbor of Q.

Now, we can eliminate Case 2.

  1. R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. 6. I sits second to the left of N. 

7. S is seated opposite the person who is immediately to the right of K.  8. L and P are not seated directly opposite to each other, and also don't sit at the ends.

9. J is the neighbour of the person who faces the one seated second to the left of T. 

This is our final arrangement,

Except for Q, all others sit at the ends.

Hence, the correct answer is Q.

28

How many persons sit between T and R in Row 2?

  1. ((a))

    0

  2. ((b))

    1

  3. ((c))

    2

  4. ((d))

    3

  5. ((e))

    4

Show Answer
Answer: ((e))

4

Given: Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

1. Q is seated three places away from U, who occupies one of the extreme ends. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

  1. The one who sits second to the left of Q sits opposite to M.

  1. M sits diagonally opposite to P, who sits third to the right of S.

  1. T sits to the right of S but is not an immediate neighbor of Q.

Now, we can eliminate Case 2.

  1. R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. 6. I sits second to the left of N. 

7. S is seated opposite the person who is immediately to the right of K.  8. L and P are not seated directly opposite to each other, and also don't sit at the ends.

9. J is the neighbour of the person who faces the one seated second to the left of T. 

This is our final arrangement,

Hence, the correct answer is 4.

29

Who among the following is seated immediately to the right of L?

  1. ((a))

    H

  2. ((b))

    I

  3. ((c))

    J

  4. ((d))

    K

  5. ((e))

    L

Show Answer
Answer: ((d))

K

Given: Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

1. Q is seated three places away from U, who occupies one of the extreme ends. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

  1. The one who sits second to the left of Q sits opposite to M.

  1. M sits diagonally opposite to P, who sits third to the right of S.

  1. T sits to the right of S but is not an immediate neighbor of Q.

Now, we can eliminate Case 2.

  1. R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. 6. I sits second to the left of N. 

7. S is seated opposite the person who is immediately to the right of K.  8. L and P are not seated directly opposite to each other, and also don't sit at the ends.

9. J is the neighbour of the person who faces the one seated second to the left of T. 

This is our final arrangement,

Hence, the correct answer is K.

30

Which of the following pair sit at the two extreme ends?

  1. ((a))

    I, U

  2. ((b))

    L, Q

  3. ((c))

    H, T

  4. ((d))

    K, P

  5. ((e))

    N, R

Show Answer
Answer: ((c))

H, T

Given: Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

1. Q is seated three places away from U, who occupies one of the extreme ends. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

  1. The one who sits second to the left of Q sits opposite to M.

  1. M sits diagonally opposite to P, who sits third to the right of S.

  1. T sits to the right of S but is not an immediate neighbor of Q.

Now, we can eliminate Case 2.

  1. R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. 6. I sits second to the left of N. 

7. S is seated opposite the person who is immediately to the right of K.  8. L and P are not seated directly opposite to each other, and also don't sit at the ends.

9. J is the neighbour of the person who faces the one seated second to the left of T. 

This is our final arrangement,

Hence, the correct answer is H, T.

31

Which among the following statement is true?

  1. ((a))

    Neither P nor Q sits directly opposite I

  2. ((b))

    S faces L

  3. ((c))

    Q and T are exactly four seats apart

  4. ((d))

    K and H are immediate neighbours

  5. ((e))

    T sits exactly one seat away from U

Show Answer
Answer: ((a))

Neither P nor Q sits directly opposite I

Given: Fourteen persons are seated in two parallel rows, with seven persons each. H, I, J, K, L, M, and N in Row 1 and facing South, while P, Q, R, S, T, U, and V in Row 2 and facing North, but not necessarily in the same order.

  1. Q is seated three places away from U, who occupies one of the extreme ends. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

  1. The one who sits second to the left of Q sits opposite to M.

  1. M sits diagonally opposite to P, who sits third to the right of S.

  1. T sits to the right of S but is not an immediate neighbor of Q.

Now, we can eliminate Case 2.

  1. R is seated opposite the person who is immediately left of N, who doesn't sit opposite Q. 6. I sits second to the left of N. 

7. S is seated opposite the person who is immediately to the right of K.  8. L and P are not seated directly opposite to each other, and also don't sit at the ends.

9. J is the neighbour of the person who faces the one seated second to the left of T. 

This is our final arrangement,

Hence, the correct answer is Neither P nor Q sits directly opposite I.

32

Which is the odd one out?

  1. ((a))

    FIR

  2. ((b))

    JMN

  3. ((c))

    BEV

  4. ((d))

    UXZ

  5. ((e))

    QTG

Show Answer
Answer: ((d))

UXZ

Logic: Second letter = First letter + 3, Third letter = Opposite of second letter

Option 1: F + 3 = I, and opposite of I = R

Option 2: J + 3 = M, and opposite of M = N

Option 3: B + 3 = E, and opposite of E = V

Option 4: U + 3 = X, and opposite of X = C ≠ Z

Hence, the correct answer is UXZ.

Direction: Read the following information carefully and answer the questions based on given information.

In a family of eight members, there are two married couples and no child has single parent. K is the brother – in – law of T. Y is the aunt of S. O is the grandson of N. Q is the daughter – in – law of K. P is not the daughter of N. S is not the brother of O. T is the uncle of Y.

33

How is Q related to N?

  1. ((a))

    Daughter

  2. ((b))

    Sister

  3. ((c))

    Mother

  4. ((d))

    Mother - in - law

  5. ((e))

    Daughter - in - law

Show Answer
Answer: ((e))

Daughter - in - law

Here, family members are K, N, O, P, Q, S, T and Y.

  1. K is the brother – in – law of T.

  2. Q is the daughter – in – law of K.

  3. T is the uncle of Y.

  1. Y is the aunt of S.

  2. O is the grandson of N.

  3. P is not the daughter of N.

  4. S is not the brother of O. (Since, there is no single parent of a child so case 1 is eliminated) Hence, the final arrangement is as follows

Hence, Q is the daughter - in - law of N.

34

Find the odd one out.

  1. ((a))

    K

  2. ((b))

    T

  3. ((c))

    P

  4. ((d))

    Y

  5. ((e))

    O

Show Answer
Answer: ((d))

Y

Here, family members are K, N, O, P, Q, S, T and Y.

  1. K is the brother – in – law of T.

  2. Q is the daughter – in – law of K.

  3. T is the uncle of Y.

  1. Y is the aunt of S.

  2. O is the grandson of N.

  3. P is not the daughter of N.

  4. S is not the brother of O. (Since, there is no single parent of a child so case 1 is eliminated) Hence, the final arrangement is as follows

Since, each person except Y is a male person whereas Y is a female person.

Hence, the odd one is Y.

35

Which of the following statement(s) is/are incorrect?

A) N is the mother of Y.

B) S is the daughter of P.

C) T is the husband of N.

  1. ((a))

    Both A and B

  2. ((b))

    Only B

  3. ((c))

    Both A and C

  4. ((d))

    Only C

  5. ((e))

    All of these

Show Answer
Answer: ((d))

Only C

Here, family members are K, N, O, P, Q, S, T and Y.

  1. K is the brother – in – law of T.

  2. Q is the daughter – in – law of K.

  3. T is the uncle of Y.

  1. Y is the aunt of S.

  2. O is the grandson of N.

  3. P is not the daughter of N.

  4. S is not the brother of O. (Since, there is no single parent of a child so case 1 is eliminated) Hence, the final arrangement is as follows

Since, N is the mother of Y. Therefore, statement A is correct.

S is the daughter of P. Therefore, statement B is correct.

T is the brother of N. Therefore, statement C is incorrect.

Hence, the incorrect statement is only C.

English Language (30 questions)

36

Read the sentence below to find out if there is any error in it. The error, if any, will be in one part of the sentence. The letter of that part is the answer. If there is no error the answer is (5). (Ignore errors in punctuation if any).

The capital on Monday (A) /recorded fresh 54 COVID-­19 cases**(B),/ the lowest since April 15 (C)/last year, and two more deaths.(D)/No error(E)**

  1. ((a))

    A

  2. ((b))

    B

  3. ((c))

    C

  4. ((d))

    D

  5. ((e))

    E

Show Answer
Answer: ((b))

B

The correct answer is option 2.

Key Points

  • The error is in Part B of the sentence, error is in use 'Fresh 54'
  • both adjectives 'fresh' and '54' describing the same noun, i.e., Covid-19 cases.
  • but while using adjectives order should be first adjective of size (54) then physical quality (Fresh)
  • Hence in the given sentence 'Fresh 54' should be replaced with '54 fresh'

Correct sentence - The capital on Monday recorded 54 fresh COVID­-19 cases, the lowest since April 15 last year, and two more deaths.

Additional Information

  • Adjective is the word which gives additional information regarding the noun.
37

Read the sentence below to find out if there is any error in it. The error, if any, will be in one part of the sentence. The letter of that part is the answer. If there is no error the answer is (5). (Ignore errors in punctuation if any).

The team have achieved (A)/ remarkable success during (B)/ the past year despite (C)/ numerous challenges. (D)/ No error (E)

  1. ((a))

    A

  2. ((b))

    B

  3. ((c))

    C

  4. ((d))

    D

  5. ((e))

    E

Show Answer
Answer: ((a))

A

The correct answer is Option 1.

 

Key Points

  • The primary issue in the sentence is the use of the plural verb "have" with the singular noun "team."
  • Collective nouns like "team" typically take a singular verb unless focusing on the individual members.
  • The correct phrase should be "The team has achieved," ensuring subject-verb agreement.
  • Thus, the error is located in part A of the sentence.

Therefore, the correct answer is A.

 

Correct Sentence: "The team has achieved remarkable success during the past year despite numerous challenges."

 

Additional Information

  • B: "remarkable success during" – This part of the sentence is grammatically correct and does not require any changes.
  • C: "the past year despite" – This part of the sentence is grammatically correct and does not require any changes.
  • D: "numerous challenges." – This part of the sentence is grammatically correct and does not require any changes.
  • No error – This would be the correct option if there were no mistakes in the sentence, but there is an error in part A.
38

Read the sentence below to find out if there is any error in it. The error, if any, will be in one part of the sentence. The letter of that part is the answer. If there is no error the answer is (5). (Ignore errors in punctuation if any).

However, the amount**(A)/ of samples tested(B)/ continued to be (C)/on the lower side(D)/No error(E)**

  1. ((a))

    A

  2. ((b))

    B

  3. ((c))

    C

  4. ((d))

    D

  5. ((e))

    E

Show Answer
Answer: ((a))

A

The correct answer is option 1.

 

  • The error is in use part A of the sentence. The error is in the use of Amount as an adjective.
  • Amount refers to how much of something there is.
  • Number refers to items we can count.
  • Hence in the given sentence amount should be replaced with number.​

Correct sentence - However, the number of samples tested continued to be on the lower side.

 

  • Adjective is the word that gives additional information regarding the noun.
39

Read the sentence below to find out if there is any error in it. The error, if any, will be in one part of the sentence. The letter of that part is the answer. If there is no error the answer is (5). (Ignore errors in punctuation if any).

Describing the prosecute version (A)/as “highly improbable”, defence lawyer**(B)/ Wills Mathews reminded the(C)/court the petitioner was discharged.(D)/ No error(E)**

  1. ((a))

    A

  2. ((b))

    B

  3. ((c))

    C

  4. ((d))

    D

  5. ((e))

    E

Show Answer
Answer: ((a))

A

The correct answer is Option 1.

 

Key Points

  • The primary issue in the sentence is the incorrect usage of the word "prosecute" in part A.
  • The correct term should be "prosecution" to accurately refer to the legal party in the context.
  • Thus, the error is located in part A of the sentence.

Therefore, the correct answer is A.

 

Correct Sentence: "Describing the prosecution version as “highly improbable,” defence lawyer Wills Mathews reminded the court the petitioner was discharged."

 

Additional Information

  • Part B: "as “highly improbable”, defence lawyer" – This part of the sentence is grammatically correct and does not require any changes.
  • Part C: "Wills Mathews reminded the" – This part of the sentence is grammatically correct and does not require any changes.
  • Part D: "court the petitioner was discharged." – This part of the sentence is grammatically correct and does not require any changes.
  • No error – This would be the correct option if there were no mistakes in the sentence, but there is an error in part A.
40

Read the sentence below to find out if there is any error in it. The error, if any, will be in one part of the sentence. The letter of that part is the answer. If there is no error the answer is (5). (Ignore errors in punctuation if any)

A third group of people would probable (A)/ accuse both the power plant (B)/ and the research institute of poisoning (C)/ the world by using and storing toxic nuclear waste (D)/ No error (E)

  1. ((a))

    A

  2. ((b))

    B

  3. ((c))

    C

  4. ((d))

    D

  5. ((e))

    E

Show Answer
Answer: ((a))

A

The correct answer is option 1.

Key Points

  • The error in part A of a sentence, the error is in usage 'Probable'
  • Here, we need to use the adverb form of 'Probable'
  • Hence we need to replace 'Probable' with 'Probably'
<br>

​Correct sentenceA third group of people would probably accuse both the power plant and the research institute of poisoning the world by using and storing toxic nuclear waste.

Additional Information

  • Adverbs usually end with 'ly'.
  • If any additional information is given regarding verbs then it is considered as an adverb.
  • In the given sentence the adverb Probably Describes the verb Accuse.
41

In the following question, two columns are given containing three phrases each. In the first column phrases are A, B, C and in the second column, the phrases are D, E, F. A phrase from the first column may or may not connect with a phrase from the second column to make a grammatically and contextually correct sentence. There are five options, four of which display the sequence(s) in which the phrases can be joined to form a grammatically and contextually correct sentence. If none of the options given forms a correct sentence after combination, select ‘None of these' as your answer.

Column(1)Column(2)
(A) He went to heckle(D) at the airport for three days.
(B) The hapless passengers were stranded(E) headlights lit the driveway.
(C) They divulge to the(F) on men not wearing jackets.
  1. ((a))

    C-D

  2. ((b))

    C-F

  3. ((c))

    B-D

  4. ((d))

    A-E and C-D

  5. ((e))

    None of the above

Show Answer
Answer: ((c))

B-D

The correct answer is B-D.

Key Points

  • Part B states 'The hapless passengers were stranded​' and part D states 'at the airport for three days'.
  • In part B, the word hapless means (especially of a person) unfortunate.
  • Here, it's said that it was very unfortunate for the passengers to get stranded at the airport for three days.
  • There is only one correct combination in the given options i.e. B-D is the correct combination.

The correct sentence is*, B-D: The hapless passengers were stranded at the airport for three days.*

Additional Information

Let us see the meanings of the words:

Other wordsMeanings
heckleinterrupt (a public speaker) with derisive or aggressive comments or abuse.
divulgemake known (private or sensitive information).
42

In the following question, two columns are given containing three phrases each. In the first column phrases are A, B, C and in the second column, the phrases are D, E, F. A phrase from the first column may or may not connect with a phrase from the second column to make a grammatically and contextually correct sentence. There are five options, four of which display the sequence(s) in which the phrases can be joined to form a grammatically and contextually correct sentence. If none of the options given forms a correct sentence after combination, select ‘None of these' as your answer.

Column(1)Column(2)
(A) We should never isolate(D) is now a dead letter.
(B)  We cannot find(E) capital punishment is a deterrent.
(C)The police are under instructions to impound(F) such machines wherever they find them.
  1. ((a))

    C-E and A-F

  2. ((b))

    A-E

  3. ((c))

    B-D

  4. ((d))

    C-F

  5. ((e))

    None of the above

Show Answer
Answer: ((d))

C-F

The correct answer is 'Option (4) → C-F'

Key Points

  • From the given options, only  the combination of phrases ' C-F' creates a correct sentence.
  • Let’s look at the sentences:
  • 'C-F' forms the sentence: “The police are under instructions to impound such machines wherever they find them.”

✔ Grammatically correct and contextually meaningful. It clearly conveys the directive given to the police.

  • 'A-E' would read: “We should never isolate capital punishment is a deterrent.”

❌ Grammatically incorrect and illogical.

  • 'B-D' would read: “We cannot find is now a dead letter.”

❌ Incorrect sentence structure and meaning.

  • 'C-E' would read: “The police are under instructions to impound capital punishment is a deterrent.”

❌ Grammatically wrong and contextually absurd.

Hence, the correct answer is Option (4).

Directions: Read the given passage carefully to answer the following questions. Each question will have five alternatives as its answer. Choose the correct option as your answer.

In the bustling city of Melbourne, Australia, a new trend had been steadily rising: cloud kitchens. These kitchens were unique in that they had no traditional shopfronts or dining areas. Instead, they focused solely on preparing food for delivery. As Jane Lawson tapped the screen of her tablet, confirming the latest batch of orders, she couldn’t help but marvel at how quickly her cloud kitchen business had taken off. With customers appreciating the convenience of home-delivered gourmet meals, her venture seemed destined for success. However, navigating the regulatory landscape for cloud kitchens was no easy task. The rules in Australia were still evolving, making it an elusive target for owners who sought to be fully compliant. Jane had spent countless hours studying food safety regulations, zoning laws, and delivery logistics requirements. She knew that ensuring her business met all these standards was crucial, not only for the survival of her kitchen but also for the safety and satisfaction of her customers. One of the regulations that often tripped up new owners was related to food hygiene. The Australian Food Safety Standards required cloud kitchens, like traditional restaurants, to adhere to strict guidelines on food storage, preparation, and delivery. Jane had done her due __________ in this area, frequently conducting internal audits to make sure everything was spotless and up to code. She had also installed temperature-controlled storage units and invested in high-quality packaging to maintain the freshness of her dishes until they reached her customers' homes. Jane's efforts didn’t stop there. She also had to navigate the complexities of zoning laws. Unlike traditional eateries, cloud kitchens often operated out of industrial spaces, which required different permits and zoning approvals. This added another layer of complexity to an already dense web of regulations. Jane sought the help of a local consultant who specialised in this area, ensuring that her business was operating within legal bounds. Despite the hurdles, Jane found the journey fulfilling. The cloud kitchen model offered her flexibility and the ability to reach a broader customer base without the overhead costs of a traditional restaurant. She could tap into the growing trend of online food delivery, leveraging technology to streamline operations and meet the demands of modern consumers. The cloud kitchen phenomenon was undoubtedly here to stay. For Jane and many other entrepreneurs, learning to navigate the elusive and ever-changing regulatory landscape remained a primary challenge. Yet, with diligence and a commitment to quality, Jane was confident that her business would not only survive but thrive in the competitive world of food delivery.

43

According to the passage, what is one of the primary challenges cloud kitchen owners face?

  1. ((a))

    Hiring and training skilled chefs

  2. ((b))

    Competing with traditional restaurants

  3. ((c))

    Navigating the regulatory landscape

  4. ((d))

    Finding reliable delivery partners

  5. ((e))

    Designing a user-friendly website

Show Answer
Answer: ((c))

Navigating the regulatory landscape

The correct answer is Option 3.

 

Key Points

  • The passage emphasizes that one of the primary challenges cloud kitchen owners face is navigating the ever-changing regulatory landscape.
  • Jane Lawson, the protagonist, spends a significant amount of time ensuring her business complies with food safety regulations, zoning laws, and delivery logistics requirements.
  • Food hygiene guidelines, zoning approvals, and various permits are specifically mentioned as regulatory hurdles that cloud kitchen owners must manage.

Therefore, the correct answer is Option 3.

 

Correct Answer: According to the passage, one of the primary challenges cloud kitchen owners face is navigating the regulatory landscape.

 

Additional Information

  • Option 1: While hiring and training skilled chefs is important, it is not highlighted as a primary challenge in the passage.
  • Option 2: Competing with traditional restaurants is also a challenge, but the passage focuses more on regulatory issues.
  • Option 4: Finding reliable delivery partners is another concern, but it is not the main focus of the passage.
  • Option 5: Designing a user-friendly website is beneficial but not identified as a primary challenge in the passage.
44

Which of the following measures did Jane take to ensure food hygiene in her cloud kitchen?

  1. ((a))

    Hired a celebrity chef

  2. ((b))

    Conducted internal audits frequently

  3. ((c))

    Offered live cooking classes

  4. ((d))

    Opened multiple kitchen locations

  5. ((e))

    Partnered with organic farms

Show Answer
Answer: ((b))

Conducted internal audits frequently

The correct answer is Option 2.

 

Key Points

  • Jane frequently conducted internal audits to ensure everything was spotless and up to code, maintaining food hygiene standards.
  • She also invested in temperature-controlled storage units and high-quality packaging to maintain the freshness of her dishes.
  • These measures helped her comply with the Australian Food Safety Standards related to food storage, preparation, and delivery.

Therefore, the correct answer is Option 2.

 

Correct Answer: Jane conducted internal audits frequently to ensure food hygiene in her cloud kitchen.

 

Additional Information

  • Option 1: There is no mention of Jane hiring a celebrity chef in the passage.
  • Option 3: Offering live cooking classes is not mentioned as a measure Jane took for food hygiene.
  • Option 4: Opening multiple kitchen locations is not related to ensuring food hygiene.
  • Option 5: Partnering with organic farms is not mentioned in the passage as a measure for food hygiene.
45

What type of spaces do cloud kitchens often operate out of, according to the passage?

  1. ((a))

    Residential areas

  2. ((b))

    Shopping malls

  3. ((c))

    Industrial spaces

  4. ((d))

    Tourist locations

  5. ((e))

    Traditional restaurants

Show Answer
Answer: ((c))

Industrial spaces

The correct answer is Option 3.

 

Key Points

  • The passage clearly states that cloud kitchens often operate out of industrial spaces.
  • These industrial spaces require different permits and zoning approvals compared to traditional eateries.
  • This adds a layer of complexity to the regulatory requirements for cloud kitchens.

Therefore, the correct answer is Option 3.

 

Correct Answer: According to the passage, cloud kitchens often operate out of industrial spaces.

 

Additional Information

  • Option 1: The passage does not mention cloud kitchens operating out of residential areas.
  • Option 2: Shopping malls are not mentioned as a typical location for cloud kitchens.
  • Option 4: Tourist locations are not indicated as common spaces for cloud kitchens to operate.
  • Option 5: Traditional restaurants are distinct from cloud kitchens and are not mentioned as their operating spaces.
46

According to the passage, which of the following statements is incorrect?

A) Jane frequently conducted internal audits to ensure food hygiene.

B) Jane did not invest in high-quality packaging for her dishes.

C) Zoning laws add complexity to cloud kitchens.

  1. ((a))

    Only A

  2. ((b))

    Only B

  3. ((c))

    Only C

  4. ((d))

    B and C

  5. ((e))

    A and B

Show Answer
Answer: ((b))

Only B

The correct answer is Option 2.

 

Key Points

  • Statement A: Jane frequently conducted internal audits to ensure food hygiene.
  • This statement is correct as it accurately reflects the context provided in the passage.
  • Statement B: Jane did not invest in high-quality packaging for her dishes.
  • The passage mentions that Jane did invest in high-quality packaging, so this statement is incorrect.
  • Statement C: Zoning laws add complexity to cloud kitchens.
  • This statement is correct as it aligns with the information provided in the passage about the complexity added by zoning laws.
  • Hence, the statement B is identified as incorrect in the context of the passage.

Therefore, the correct answer is: ‘Only B’.

47

What will fit in the blank taken from the passage: "Jane had done her due __________ in this area, frequently conducting internal audits to make sure everything was spotless and up to code."

  1. ((a))

    diligence

  2. ((b))

    research

  3. ((c))

    inquiry

  4. ((d))

    analysis

  5. ((e))

    examination

Show Answer
Answer: ((a))

diligence

The correct answer is 'diligence'.

 

Key Points

  • The word "diligence" means careful and persistent work or effort. (परिश्रम)
  • In the context of the passage, Jane ensures that her cloud kitchen adheres to all food hygiene regulations through diligent efforts such as frequently conducting internal audits.
  • The other options: "research," "inquiry," "analysis," and "examination" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: Jane had done her due diligence in this area, frequently conducting internal audits to make sure everything was spotless and up to code.

Additional Information

  • Research (अनुसंधान): means the systematic investigation into and study of materials and sources in order to establish facts and reach new conclusions.
  • Inquiry (जांच): means an act of asking for information.
  • Analysis (विश्लेषण): means detailed examination of the elements or structure of something.
  • Examination (परीक्षा): means a detailed inspection or study.
48

Which of the following words is similar in meaning to "tap" as used in the passage?

  1. ((a))

    strike

  2. ((b))

    overlook

  3. ((c))

    touch

  4. ((d))

    examine

  5. ((e))

    ignore

Show Answer
Answer: ((c))

touch

The correct answer is: touch.

Key Points

  • The word "tap" as used in the passage means to touch lightly or gently, especially as part of using a device. (छूना)
  • Example: She tapped the icon on her phone to open the app.
  • "Touch" refers to coming into contact with something lightly. (स्पर्श)
  • Example: Please touch the screen to start the game.
  • Hence, we can infer that the word "tap" is similar in meaning to "touch".

Therefore, the correct answer is: touch.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

  • Strike (मारना): To hit or dash.
  • Example: The boxer aimed to strike his opponent with a powerful punch.
  • Overlook (अनदेखा करना): To ignore or fail to notice something.
  • Example: It's easy to overlook minor spelling errors when you're editing.
  • Examine (जांचना): To inspect or scrutinise carefully.
  • Example: The doctor will examine your eyes to check for any issues.
  • Ignore (अनदेखा करना): To refuse to take notice of or acknowledge.
  • Example: She chose to ignore the negative comments and focused on her success.
49

Which of the following words is similar in meaning to "done" as used in the passage?

  1. ((a))

    accomplished

  2. ((b))

    began

  3. ((c))

    ignored

  4. ((d))

    questioned

  5. ((e))

    delayed

Show Answer
Answer: ((a))

accomplished

The correct answer is: accomplished.

Key Points

  • The word "done" in the context of the passage means finished or completed. (पूरा किया हुआ)
  • Example: She has done her homework with great effort.
  • "Accomplished" means having achieved or completed successfully. (सफलता प्राप्त करना)
  • Example: He accomplished his mission with dedication and hard work.
  • Hence, we can infer that "done" is similar in meaning to "accomplished".

Therefore, the correct answer is: accomplished.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

  • Began (शुरू किया): To start or commence.
  • Example: She began her journey early in the morning.
  • Ignored (अनदेखा किया): To refuse to take notice of or acknowledge.
  • Example: He ignored the warning signs on the road.
  • Questioned (सवाल किया): To ask questions or express doubt about something.
  • Example: The students questioned the logic behind the exam rules.
  • Delayed (विलंबित किया): To postpone or put off to a later time.
  • Example: The flight was delayed due to bad weather.
50

Which of the following words is opposite in meaning to "elusive" as used in the passage?

  1. ((a))

    comprehensive

  2. ((b))

    easy

  3. ((c))

    practical

  4. ((d))

    attainable

  5. ((e))

    explicit

Show Answer
Answer: ((d))

attainable

The correct answer is: Option 4 (Attainable).

Key Points

  • The word "elusive" means difficult to find, achieve, understand, or obtain. (दुर्लभ/पकड़ में न आने वाला/प्राप्त करना कठिन)
  • Example: Success remained elusive despite his continuous efforts.
  • The correct word is "attainable", which means capable of being achieved, reached, or obtained. (प्राप्य/हासिल करने योग्य)
  • Example: With proper planning and dedication, the target is attainable.
  • "Elusive" describes something that is difficult to achieve or obtain, whereas "attainable" describes something that can be achieved or obtained. Therefore, they are opposite in meaning.

Therefore, the correct answer is: Option 4 (Attainable).

Additional Information

Here are the other options explained along with their Hindi meanings:

  • Option 1: Comprehensive (व्यापक/संपूर्ण): Including all or nearly all aspects of something.
  • Example: The report provides a comprehensive analysis of the issue.
  • Option 2: Easy (आसान/सरल): Not difficult to do, understand, or achieve.
  • Example: The examination was relatively easy for the well-prepared students.
  • Option 3: Practical (व्यावहारिक/उपयोगी): Suitable for actual use or likely to be effective in real situations.
  • Example: She offered a practical solution to the problem.
  • Option 5: Explicit (स्पष्ट/सुस्पष्ट): Clearly stated or expressed without ambiguity.
  • Example: The teacher gave explicit instructions to the students.
51

Direction: Evaluate the following word, accompanied by three sentences containing it. Determine the sentence(s) that accurately convey the meaning of the given word.

Dark horse

A. The unknown candidate turned out to be a dark horse, winning the election by a large margin.

B. She wore a dark horse dress to the party and received many compliments.

C. The latest novel by the author is a dark horse, becoming a bestseller unexpectedly.

  1. ((a))

    Only A

  2. ((b))

    Both A & B

  3. ((c))

    Both A & C

  4. ((d))

    All A, B & C

  5. ((e))

    None of these

Show Answer
Answer: ((c))

Both A & C

The correct answer is option 3.

Key Points

  • To answer this question, let's first understand the meaning of the word given in the question:
  • Dark horse: a candidate or competitor about whom little is known but who unexpectedly wins or succeeds. (अप्रत्याशित विजेता या सफल व्यक्ति)
  • Now, let's examine the given sentences:
  • Sentence A: The unknown candidate turned out to be a dark horse, winning the election by a large margin.
  • This sentence correctly uses the term "dark horse" to describe an unexpected winner in an election.
  • Sentence B: She wore a dark horse dress to the party and received many compliments.
  • This sentence does not use the term "dark horse" correctly, as it does not fit the meaning of an unexpected winner or success.
  • Sentence C: The latest novel by the author is a dark horse, becoming a bestseller unexpectedly.
  • This sentence accurately uses the term "dark horse" to describe a novel that became an unexpected bestseller.
  • So, both Sentence A and Sentence C correctly use the term "dark horse" to illustrate different contexts of unexpected success.

Therefore, the correct answer is Both A and C.

52

Directions: In the following sentence, four words given in bold are marked as A, B, C, and D, which are possible pairs to be interchanged. Choose the pair(s) of words that need to be interchanged to make the sentence grammatically correct and meaningful. If no interchange is required, mark option 5 i.e., "No interchange required" as your answer.

The environmental (A) minister had told the Rajya Sabha that the new legislation (B) will give a fresh impetus to industries (C) and also boost health (D) protection.

  1. ((a))

    B-C

  2. ((b))

    A-D

  3. ((c))

    A-C

  4. ((d))

    A-D and B-C

  5. ((e))

    No Interchange required

Show Answer
Answer: ((b))

A-D

The correct answer is option 2.

Key Points

The words “environmental (A)” and “health (D)” need to be interchanged.

  • The correct phrase is “health minister”, not “environmental minister.”
  • The legislation is logically intended to boost environment protection, not “health protection” in this context.
  • After interchange: “The health minister… boost environment protection” — which is meaningful and grammatically correct.

Therefore, the correct answer is option 2 (A-D).

Additional Information

  • Option 1 (B-C): Interchanging “legislation” and “industries” distorts the meaning.
  • Option 3 (A-C): Creates illogical combinations.
  • Option 4: Both interchanges are unnecessary and incorrect.
  • Option 5: Incorrect because the original sentence is logically inconsistent.
53

Directions: In the following sentence, four words given in bold are marked as A, B, C, and D, which are possible pairs to be interchanged. Choose the pair(s) of words that need to be interchanged to make the sentence grammatically correct and meaningful. If no interchange is required, mark option 5 i.e., "No interchange required" as your answer.

The judiciary (A) must respect the powers (B) of separation (C) between organs of the state.(D)

  1. ((a))

    A-D

  2. ((b))

    B-C

  3. ((c))

    A-B

  4. ((d))

    B-C and A-D

  5. ((e))

    No interchange required

Show Answer
Answer: ((b))

B-C

The correct answer is option 2.

Key Points Icon

Key Points

The judiciary must respect the separation of powers between organs of the state.

  • The pair of words B-C needs to be interchanged to make the sentence grammatically correct.
  • After the interchange:
  • "The judiciary must respect the separation (C) of powers (B) between organs of the state."
54

Directions: In the following sentence, four words given in bold are marked as A, B, C, and D, which are possible pairs to be interchanged. Choose the pair(s) of words that need to be interchanged to make the sentence grammatically correct and meaningful. If no interchange is required, mark option 5 i.e., "No interchange required" as your answer.

The Chief Justice passed (A) that sitting on Bills highlighted (B) by a competent (C) legislature undermines (D) democracy.

  1. ((a))

    A-B

  2. ((b))

    B-D

  3. ((c))

    A-C and B-D

  4. ((d))

    A-D

  5. ((e))

    No interchange required

Show Answer
Answer: ((a))

A-B

The correct answer is: Option 1 (A-B).

Key Points

  • The word "passed" means to approve or formally accept something, especially in the context of laws or bills. (पारित करना)
  • Example: The parliament passed the new education bill yesterday.
  • The word "highlighted" means to emphasize or draw attention to something important. (प्रमुख करना/उजागर करना)
  • Example: The report highlighted the need for urgent reforms in the healthcare sector.
  • Hence, the correct interchange is between A (passed) and B (highlighted), making the sentence: The Chief Justice highlighted that sitting on Bills passed by a competent legislature undermines democracy.

Therefore, the correct answer is: Option 1 (A-B).

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

  • Option 2 (B-D): Incorrect, because "Bills undermines by a competent legislature" is grammatically wrong. ("Undermines" = कमजोर करना)
  • Example: Corruption undermines the trust of citizens in democracy.
  • Option 3 (A-C and B-D): Incorrect, because swapping "passed" with "competent" and "highlighted" with "undermines" makes the sentence meaningless. ("Competent" = सक्षम)
  • Example: She is a competent lawyer who handles complex cases with ease.
  • Option 4 (A-D): Incorrect, because "The Chief Justice undermines that sitting on Bills..." is illogical. ("Undermines" = कमजोर करना)
  • Example: Spreading false information undermines public confidence.
  • Option 5 (No interchange required): Incorrect, because the original sentence is grammatically flawed and does not convey the intended meaning.
55

Directions: In the following sentence, four words given in bold are marked as A, B, C, and D, which are possible pairs to be interchanged. Choose the pair(s) of words that need to be interchanged to make the sentence grammatically correct and meaningful. If no interchange is required, mark option 5 i.e., "No interchange required" as your answer.

Justice Officer solved (A) whether every judicial remedies (B) could be asked (C) through constitutional problem(D)

  1. ((a))

    A-D

  2. ((b))

    B-D

  3. ((c))

    A-C and B-D

  4. ((d))

    A-C

  5. ((e))

    No interchange required

Show Answer
Answer: ((c))

A-C and B-D

The correct answer is option 3.

Key Points

  • The given sentence is: Justice officer solved (A) whether every judicial remedies (B) could be asked (C) through constitutional problem (D).
  • The word ‘solved’ (A) does not fit correctly in the sentence as it refers to resolving an issue, while the correct meaning intended here is to inquire or determine.
  • The word ‘problem’ (D) also does not fit correctly in the sentence in its current position. Instead, it should replace (A).
  • Similarly, ‘remedies’ (B) and ‘asked’ (C) are misplaced and need to be swapped to make the sentence meaningful.

Correct Sentence after interchange: Justice officer asked (A) whether every judicial problem (D) could be solved (C) through constitutional remedies (B).

Pairs to be interchanged: A-C and B-D.

56

Directions: Select the most appropriate word to fill in the blank.

The job of a railway officer is not meant for those _______ for a fixed hours work profile.

  1. ((a))

    Astonishing

  2. ((b))

    Looking

  3. ((c))

    Allotting

  4. ((d))

    Surprising

  5. ((e))

    Learning

Show Answer
Answer: ((b))

Looking

The correct answer is 'Looking.'

Key Points

  • The given sentence is saying that the job of a railway officer is not for those who regard or think of it as a fixed hours work profile.
  • Therefore, the most appropriate word to be filled in the blank is 'Looking'.
  • Also, the use of the phrase ''not meant'' in the sentence indicates the use of the word 'looking' in the blank.
  • The word 'Looking' means To think of or regard in a specified way.
  • Example: We are looking for a better understanding between the two nations.

Hence, the correct answer is option 2.

Complete Sentence: The job of a railway officer is not meant for those looking for a fixed hours work profile.

Additional Information

  • Let us explore  the other options:
  • Astonishing means Extremely surprising or impressive; amazing.
  • Allotting means To give a share of work, time, etc. to somebody or something.
  • Surprising means Causing surprise; unexpected.
  • Learning means Knowledge that you get from studying.
57

Choose the word for the given options that could fit in the blank correctly.

The young man worked hard in _______ of his famous father.

  1. ((a))

    copying

  2. ((b))

    ape

  3. ((c))

    simulation

  4. ((d))

    emulation

  5. ((e))

    multiplication

Show Answer
Answer: ((d))

emulation

The correct answer is emulation.

Key Points

  • The blank gives the answer to the efforts that the young man made imitating his famous father.
  • Now let's understand the meaning of all options:
  • Copying: An instance of the making of a copy
  • Ape: Imitate uncritically and in every aspect
  • Simulation: The act of giving a false appearance
  • Emulation: Effort to equal or surpass another
  • Multiplication: The act of producing offspring or multiplying by such production.
  • Hence, option 4 is the most appropriate answer.

The correct sentence is: The young man worked hard in emulation of his fam**ous father.

58

Choose the word for the given options that could fit in the blank correctly.

I want to________ tonight or early tomorrow morning as this place is toxic.

  1. ((a))

    go away

  2. ((b))

    go after

  3. ((c))

    go down

  4. ((d))

    go for

  5. ((e))

    go off

Show Answer
Answer: ((a))

go away

The correct answer is 'go away'.

Key Points

  • Go away: Leave a place
  • Ex: Go away before I start to cry
  • Go after: Pursue (an object or a goal)
  • Ex: Emma went after her dreams and now she is an actress.
  • Go down: Decrease; reduce
  • Ex: The price of property has gone down a bit lately.
  • Go for: Try to achieve or attain
  • Ex: Jack trained hard and decided to go for the gold medal.
  • Go off: Explode
  • Ex: A bomb went off in a crowded restaurant.
  • Here in the sentence, the author wants to leave the place tonight or early tomorrow morning, hence, 'go away' is the most appropriate choice for the blank.
  • The correct answer is option 1.

The correct sentence: I want to go away tonight or early tomorrow morning as this place is toxic.

59

Directions: Choose the word for the given options that could fit in the blank correctly.

Last year the company looked _________ but in recent weeks it has begun to have problems.

  1. ((a))

    Incomprehensible

  2. ((b))

    Invincible

  3. ((c))

    Incorrigible

  4. ((d))

    Impressive

  5. ((e))

    Impossible

Show Answer
Answer: ((d))

Impressive

The correct answer is 'Impressive'.

Key Points

  • The sentence makes it understood that we need an adjective that qualifies the noun company and it contrasts the meaning of the second clause.
  • Let's understand the meaning of options:
    • Invincible(adj) - Incapable of being overcome or subdued
  • Incomprehensible(adj) - Incapable of being explained or accounted for
  • Incorrigible(adj) - Impervious to correction by punishment
  • Impressive(adj) - Making a strong or vivid impression
  • Impossible(adj) - Not capable of occurring or being accomplished or dealt with
  • Hence, the correct answer is option 4.


The correct sentence is- Last year the company looked Impressive but in recent weeks it has begun to have problems.

60

Directions: Choose the word for the given options that could fit in the blank correctly.

The paint is starting to_________ the wall in the kitchen.

  1. ((a))

    come over

  2. ((b))

    come back

  3. ((c))

    come across

  4. ((d))

    come along

  5. ((e))

    come off

Show Answer
Answer: ((e))

come off

The correct answer is 'come off'.

Key Points

  • Come off: when something becomes separated or unstuck from another thing
  • Ex: "His retina came off and he had to be rushed into surgery"
  • Come across: find something by accident
  • Ex: "I came across these old photos recently"
  • Come along: accompany someone when going somewhere
  • Ex: We’re going to get ice cream. Want to come along?
  • Come back: return
  • Ex: He’s still hoping his ex-girlfriend will come back to him, even after all these years.
  • Come over: to seem to be a particular type of person:
  • Ex: I watched the interview and felt he came over as quite arrogant.
  • In the given sentence, it is clear that the paint started to separate from the wall. Here 'came off' is the right choice for the blank.
  • Hence, the correct answer is option 5.

The correct sentence: The paint is starting to come off the wall in the kitchen.

Directions: Rearrange the following sentences in the proper sequence to form a meaningful paragraph and then answer the questions given below.

<br>

A. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life.

B. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention.

C. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments.

D. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development.

E. Learning multiple languages offers a myriad of cognitive benefits beyond mere communication

61

Which of the following should be the FIRST sentence after rearrangement?

  1. ((a))

    E

  2. ((b))

    D

  3. ((c))

    B

  4. ((d))

    A

  5. ((e))

    C

Show Answer
Answer: ((a))

E

The correct answer is Option 1 (E).

 

Key Points

  • The paragraph focuses on the cognitive benefits of learning multiple languages and their impact on brain development, moving from a general statement to specific advantages and a concluding summary.
  • Sentence E is the first sentence as it introduces the main topic: the broad cognitive benefits of learning multiple languages.
  • "Learning multiple languages offers a myriad of cognitive benefits beyond mere communication."
  • Sentence D follows as it narrows the focus to "brain development" and cites research, providing a scientific basis for the claims.
  • "Research consistently shows that bilingualism and multilingualism can significantly enhance brain development."
  • Sentence B is the third sentence because it provides concrete examples of the cognitive improvements mentioned in D (problem-solving, multitasking, memory).
  • "For instance, it improves problem-solving abilities, multitasking skills, and even memory retention."
  • Sentence C is the fourth as it further expands on the positive outcomes resulting from "this enhanced cognitive flexibility" (referring to the benefits listed in B).
  • "This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments."
  • Sentence A is the fifth (last) as it provides a conclusive summary of the overall positive impact of linguistic diversity.
  • "Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."
  • The correct sequence is E D B C A.

 

Coherent paragraph after rearrangement:

"Learning multiple languages offers a myriad of cognitive benefits beyond mere communication. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."

62

Which of the following should be the SECOND sentence after rearrangement?

  1. ((a))

    D

  2. ((b))

    C

  3. ((c))

    B

  4. ((d))

    E

  5. ((e))

    A

Show Answer
Answer: ((a))

D

The correct answer is Option 1 (D).

 

Key Points

  • The paragraph focuses on the cognitive benefits of learning multiple languages and their impact on brain development, moving from a general statement to specific advantages and a concluding summary.
  • Sentence E is the first sentence as it introduces the main topic: the broad cognitive benefits of learning multiple languages.
  • "Learning multiple languages offers a myriad of cognitive benefits beyond mere communication."
  • Sentence D follows as it narrows the focus to "brain development" and cites research, providing a scientific basis for the claims.
  • "Research consistently shows that bilingualism and multilingualism can significantly enhance brain development."
  • Sentence B is the third sentence because it provides concrete examples of the cognitive improvements mentioned in D (problem-solving, multitasking, memory).
  • "For instance, it improves problem-solving abilities, multitasking skills, and even memory retention."
  • Sentence C is the fourth as it further expands on the positive outcomes resulting from "this enhanced cognitive flexibility" (referring to the benefits listed in B).
  • "This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments."
  • Sentence A is the fifth (last) as it provides a conclusive summary of the overall positive impact of linguistic diversity.
  • "Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."
  • The correct sequence is E D B C A.

 

Coherent paragraph after rearrangement:

"Learning multiple languages offers a myriad of cognitive benefits beyond mere communication. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."

63

Which of the following should be the THIRD sentence after rearrangement?

  1. ((a))

    E

  2. ((b))

    C

  3. ((c))

    D

  4. ((d))

    B

  5. ((e))

    A

Show Answer
Answer: ((d))

B

The correct answer is Option 4 (B).

 

Key Points

  • The paragraph focuses on the cognitive benefits of learning multiple languages and their impact on brain development, moving from a general statement to specific advantages and a concluding summary.
  • Sentence E is the first sentence as it introduces the main topic: the broad cognitive benefits of learning multiple languages.
  • "Learning multiple languages offers a myriad of cognitive benefits beyond mere communication."
  • Sentence D follows as it narrows the focus to "brain development" and cites research, providing a scientific basis for the claims.
  • "Research consistently shows that bilingualism and multilingualism can significantly enhance brain development."
  • Sentence B is the third sentence because it provides concrete examples of the cognitive improvements mentioned in D (problem-solving, multitasking, memory).
  • "For instance, it improves problem-solving abilities, multitasking skills, and even memory retention."
  • Sentence C is the fourth as it further expands on the positive outcomes resulting from "this enhanced cognitive flexibility" (referring to the benefits listed in B).
  • "This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments."
  • Sentence A is the fifth (last) as it provides a conclusive summary of the overall positive impact of linguistic diversity.
  • "Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."
  • The correct sequence is E D B C A.

 

Coherent paragraph after rearrangement:

"Learning multiple languages offers a myriad of cognitive benefits beyond mere communication. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."

64

Which of the following should be the FOURTH sentence after rearrangement?

  1. ((a))

    B

  2. ((b))

    D

  3. ((c))

    A

  4. ((d))

    E

  5. ((e))

    C

Show Answer
Answer: ((e))

C

The correct answer is Option 5 (C).

 

Key Points

  • The paragraph focuses on the cognitive benefits of learning multiple languages and their impact on brain development, moving from a general statement to specific advantages and a concluding summary.
  • Sentence E is the first sentence as it introduces the main topic: the broad cognitive benefits of learning multiple languages.
  • "Learning multiple languages offers a myriad of cognitive benefits beyond mere communication."
  • Sentence D follows as it narrows the focus to "brain development" and cites research, providing a scientific basis for the claims.
  • "Research consistently shows that bilingualism and multilingualism can significantly enhance brain development."
  • Sentence B is the third sentence because it provides concrete examples of the cognitive improvements mentioned in D (problem-solving, multitasking, memory).
  • "For instance, it improves problem-solving abilities, multitasking skills, and even memory retention."
  • Sentence C is the fourth as it further expands on the positive outcomes resulting from "this enhanced cognitive flexibility" (referring to the benefits listed in B).
  • "This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments."
  • Sentence A is the fifth (last) as it provides a conclusive summary of the overall positive impact of linguistic diversity.
  • "Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."
  • The correct sequence is E D B C A.

 

Coherent paragraph after rearrangement:

"Learning multiple languages offers a myriad of cognitive benefits beyond mere communication. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."

65

Which of the following should be the FIFTH sentence after rearrangement?

  1. ((a))

    E

  2. ((b))

    D

  3. ((c))

    A

  4. ((d))

    B

  5. ((e))

    C

Show Answer
Answer: ((c))

A

The correct answer is Option 3 (A).

 

Key Points

  • The paragraph focuses on the cognitive benefits of learning multiple languages and their impact on brain development, moving from a general statement to specific advantages and a concluding summary.
  • Sentence E is the first sentence as it introduces the main topic: the broad cognitive benefits of learning multiple languages.
  • "Learning multiple languages offers a myriad of cognitive benefits beyond mere communication."
  • Sentence D follows as it narrows the focus to "brain development" and cites research, providing a scientific basis for the claims.
  • "Research consistently shows that bilingualism and multilingualism can significantly enhance brain development."
  • Sentence B is the third sentence because it provides concrete examples of the cognitive improvements mentioned in D (problem-solving, multitasking, memory).
  • "For instance, it improves problem-solving abilities, multitasking skills, and even memory retention."
  • Sentence C is the fourth as it further expands on the positive outcomes resulting from "this enhanced cognitive flexibility" (referring to the benefits listed in B).
  • "This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments."
  • Sentence A is the fifth (last) as it provides a conclusive summary of the overall positive impact of linguistic diversity.
  • "Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."
  • The correct sequence is E D B C A.

 

Coherent paragraph after rearrangement:

"Learning multiple languages offers a myriad of cognitive benefits beyond mere communication. Research consistently shows that bilingualism and multilingualism can significantly enhance brain development. For instance, it improves problem-solving abilities, multitasking skills, and even memory retention. This enhanced cognitive flexibility can also lead to better academic performance and adaptability in diverse environments. Ultimately, embracing linguistic diversity contributes to a sharper mind and a more enriched life."

Quantitative Aptitude (35 questions)

Number of lab assistant in college A is 20 less than the number of professors in same college. Ratio of number of lab assistant and professor in college C is 4:7. Ratio of number of lab assistant in college B and A is 5:4. Number of professors in college B is 37.5% more than the number of professors in college A. Number of lab assistant in college C is 40% more than the number of lab assistant in college A. Total number of lab assistant in three college together is 73.

66

What is the ratio of number of Lab Assistants in College A to Professors in College A?

  1. ((a))

    1:2

  2. ((b))

    2:3

  3. ((c))

    3:5

  4. ((d))

    5:4

  5. ((e))

    1:3

Show Answer
Answer: ((a))

1:2

Common Calculation

Let the number of lab assistants in College A be L _A.

Then, lab assistants in College B = (5/4) * L _A.

Lab assistants in College C = (7/5) * L _A.

According to the question: L _A + (5/4)L _A + (7/5)L _A = 73.

=> L _A × (1 + 1.25 + 1.4) = 73.

=> L _A × 3.65 = 73.

=> L _A = 20.

So, L _B = 25, LC = 28.

Professors in College A: P _A = L _A + 20 = 40.

Professors in College B: P _ B = 1.375 × P _A = 55.

Professors in College C: PC = (7/4) * L _C = 49.

Final distribution:

College A: 20 lab assistants, 40 professors

College B: 25 lab assistants, 55 professors

College C: 28 lab assistants, 49 professors

 

CollegeNumber of Lab AssistantNumber of Professor
A2040
B2555
C2849

 

Calculation

Lab Assistants (A) = 20

Professors (A) = 40

Ratio = 20 : 40 = 1 : 2

67

By how many does the number of Professors in College B exceed the number of Lab Assistants in the same college?

  1. ((a))

    30

  2. ((b))

    34

  3. ((c))

    35

  4. ((d))

    42

  5. ((e))

    37

Show Answer
Answer: ((a))

30

Common Calculation

Let the number of lab assistants in College A be L _A.

Then, lab assistants in College B = (5/4) * L _A.

Lab assistants in College C = (7/5) * L _A.

According to the question: L _A + (5/4)L _A + (7/5)L _A = 73.

=> L _A × (1 + 1.25 + 1.4) = 73.

=> L _A × 3.65 = 73.

=> L _A = 20.

So, L _B = 25, LC = 28.

Professors in College A: P _A = L _A + 20 = 40.

Professors in College B: P _ B = 1.375 × P _A = 55.

Professors in College C: PC = (7/4) * L _C = 49.

Final distribution:

College A: 20 lab assistants, 40 professors

College B: 25 lab assistants, 55 professors

College C: 28 lab assistants, 49 professors

 

CollegeNumber of Lab AssistantNumber of Professor
A2040
B2555
C2849

 

Calculation

Professors (B) = 55

Lab Assistants (B) = 25

Difference = 55 – 25 = 30

68

What is the percentage of Professors in College C out of the total number of Professors in all three colleges together?

  1. ((a))

    34%

  2. ((b))

    32%

  3. ((c))

    39%

  4. ((d))

    44%

  5. ((e))

    31%

Show Answer
Answer: ((a))

34%

Common Calculation

Let the number of lab assistants in College A be L _A.

Then, lab assistants in College B = (5/4) * L _A.

Lab assistants in College C = (7/5) * L _A.

According to the question: L _A + (5/4)L _A + (7/5)L _A = 73.

=> L _A × (1 + 1.25 + 1.4) = 73.

=> L _A × 3.65 = 73.

=> L _A = 20.

So, L _B = 25, LC = 28.

Professors in College A: P _A = L _A + 20 = 40.

Professors in College B: P _ B = 1.375 × P _A = 55.

Professors in College C: PC = (7/4) * L _C = 49.

Final distribution:

College A: 20 lab assistants, 40 professors

College B: 25 lab assistants, 55 professors

College C: 28 lab assistants, 49 professors

 

CollegeNumber of Lab AssistantNumber of Professor
A2040
B2555
C2849

 

Calculation

Total Professors = 40 + 55 + 49 = 144

Professors in C = 49

% = (49 / 144) × 100 ≈ 34.03%

69

Suppose a new College D has 3 Lab Assistants more than C and 20 professor more than A. Find the average number of Lab Assistants across all four colleges and compare it with the average number of Professors. By how many is the average of Professors greater?

  1. ((a))

    39

  2. ((b))

    44

  3. ((c))

    25

  4. ((d))

    21

  5. ((e))

    22

Show Answer
Answer: ((c))

25

Common Calculation

Let the number of lab assistants in College A be L _A.

Then, lab assistants in College B = (5/4) * L _A.

Lab assistants in College C = (7/5) * L _A.

According to the question: L _A + (5/4)L _A + (7/5)L _A = 73.

=> L _A × (1 + 1.25 + 1.4) = 73.

=> L _A × 3.65 = 73.

=> L _A = 20.

So, L _B = 25, LC = 28.

Professors in College A: P _A = L _A + 20 = 40.

Professors in College B: P _ B = 1.375 × P _A = 55.

Professors in College C: PC = (7/4) * L _C = 49.

Final distribution:

College A: 20 lab assistants, 40 professors

College B: 25 lab assistants, 55 professors

College C: 28 lab assistants, 49 professors

 

CollegeNumber of Lab AssistantNumber of Professor
A2040
B2555
C2849

 

Calculation

Total Lab Assistants = 20 + 25 + 28 + 31 = 104

→ Average = 104 ÷ 4 = 26

Total Professors = 40 + 55 + 49 + 60 = 204

→ Average = 204 ÷ 4 = 51

Difference = 51 – 26 = 25

70

If 20% of Professors in College B are transferred to College A and 10 professors to college C, then what will be the new ratio of Professors in College A to those in College B?

  1. ((a))

    3:2

  2. ((b))

    2:1

  3. ((c))

    5:4

  4. ((d))

    3:7

  5. ((e))

    7:3

Show Answer
Answer: ((a))

3:2

Common Calculation

Let the number of lab assistants in College A be L _A.

Then, lab assistants in College B = (5/4) * L _A.

Lab assistants in College C = (7/5) * L _A.

According to the question: L _A + (5/4)L _A + (7/5)L _A = 73.

=> L _A × (1 + 1.25 + 1.4) = 73.

=> L _A × 3.65 = 73.

=> L _A = 20.

So, L _B = 25, LC = 28.

Professors in College A: P _A = L _A + 20 = 40.

Professors in College B: P _ B = 1.375 × P _A = 55.

Professors in College C: PC = (7/4) * L _C = 49.

Final distribution:

College A: 20 lab assistants, 40 professors

College B: 25 lab assistants, 55 professors

College C: 28 lab assistants, 49 professors

 

CollegeNumber of Lab AssistantNumber of Professor
A2040
B2555
C2849

 

Calculation

Professors in B = 55 → 20% = 11

→ transfer = 11

→ New Professors in A = 40 + 11 = 51

→ New Professors in B = 55 – 11 - 10 = 34

→ ​Ratio = 51:34 = 3:2

71

Three persons A,  B, and C enter into the business by investing with the ratio 8 : 5 : 6 respectively, after one year A invests more Rs. 5300, B withdraws Rs. 4200,and C invest more Rs. 19000. Now the ratio of the investment 5 : 3 : 4 respectively, then what amount A invested initially (Approximately)?

  1. ((a))

    295200

  2. ((b))

    478955

  3. ((c))

    286099

  4. ((d))

    243900

  5. ((e))

    None of these

Show Answer
Answer: ((a))

295200

Shortcut Trick

Let initial investments be 8x, 5x, and 6x. After changes, ratio is 5 : 3 : 4.

Using A and B: (8x + 5300) ÷ (5x − 4200) = 5 ÷ 3.

24x + 15900 = 25x − 21000 ⇒ x = 36900.

Initial investment of A = 8x = 8 × 36900 = 295200.

Check with C: (6 × 36900 + 19000) = 240400. Ratio B:C = (5 × 36900 − 4200) : 240400 = 180300 : 240400 = 3 : 4 (Satisfied).

∴ The correct answer is 295200.

Alternate Method

Given → Initial ratio A:B:C = 8 : 5 : 6. Final ratio 5 : 3 : 4. Formulas: New Investment = Initial Investment + Addition − Withdrawal.

⇒ Let the initial investments of A, B, and C be 8x, 5x, and 6x respectively. ⇒ New investment of A = 8x + 5300. ⇒ New investment of B = 5x − 4200. ⇒ According to the question: (8x + 5300) / (5x − 4200) = 5 / 3. ⇒ 3 × (8x + 5300) = 5 × (5x − 4200). ⇒ 24x + 15900 = 25x − 21000. ⇒ 25x − 24x = 15900 + 21000 ⇒ x = 36900. ⇒ Initial amount invested by A = 8x = 8 × 36900 = 295200.

∴ The correct answer is 295200.

Additional Information

Partnership Ratios

In a Partnership, the ratio of profits is generally the ratio of the product of (Investment × Time). If time is constant, Profit Ratio = Investment Ratio.

Variable Management

When solving problems with multiple changes, equate any two parts of the ratio (e.g., A/B or B/C) to find the common multiplier x.

72

The ratio of the cost of a Bike to a Car is 5:6. Person B purchased 12 Bikes and 2x Cars, while Person A purchased 9 Bikes and x Cars. If the total amount paid by Person B is 60% more than that of the total amount paid by Person A, then find the value of x.

  1. ((a))

    7

  2. ((b))

    6

  3. ((c))

    5

  4. ((d))

    4

  5. ((e))

    3

Show Answer
Answer: ((c))

5

Shortcut Trick

Let the cost of a Bike be 5 and a Car be 6.

Total cost for Person A = (9 × 5) + (x × 6) = 45 + 6x.

Total cost for Person B = (12 × 5) + (2x × 6) = 60 + 12x.

Since B paid 60% more than A, the ratio of B to A is 160 : 100 or 8 : 5.

Equating ratios: (60 + 12x) ÷ (45 + 6x) = 8 ÷ 5.

300 + 60x = 360 + 48x ⇒ 12x = 60 ⇒ x = 5.

∴ The correct answer is 5.

Alternate Method

Given: Ratio of Cost Price (CP) of Bike : Car = 5 : 6. Let CPBike = 5k and CPCar = 6k. Formulas: Total Cost = (QuantityBike × CPBike) + (QuantityCar × CPCar) | AmountB = AmountA × (1 + 60/100).

⇒ Amount paid by Person A = (9 × 5k) + (x × 6k) = k(45 + 6x). ⇒ Amount paid by Person B = (12 × 5k) + (2x × 6k) = k(60 + 12x). ⇒ According to the question: k(60 + 12x) = 1.6 × k(45 + 6x). ⇒ 60 + 12x = 72 + 9.6x. ⇒ 12x − 9.6x = 72 − 60. ⇒ 2.4x = 12 ⇒ x = 12 ÷ 2.4 = 5.

∴ The correct answer is 5.

Additional Information

Ratio and Proportion

When quantities are given in ratio (a:b), we can assume actual values as ax and bx to simplify calculation.

Percentage Increase

A value increased by 60% is equivalent to multiplying the original value by 1.6 or the fraction 8/5.

73

What approximate value should come in the place of question mark (?) in the following question?

344.98 - [551.98 ÷ 23.08] + 27.98 = ? - 13.99

  1. ((a))

    363

  2. ((b))

    343

  3. ((c))

    327

  4. ((d))

    377

  5. ((e))

    393

Show Answer
Answer: ((a))

363

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

344.98 - [551.98 ÷ 23.08] + 27.98 = ? - 13.99

⇒ 345 - [552 ÷ 23] + 28 = ? - 14

⇒ 345 - 24 + 28 = ? - 14

⇒ 349 = ? - 14

⇒ 349 + 14 = ?

∴ ? = 363

74

What approximate value should come in the place of question mark (?) in the following question?

(55.89 + 11.94 × 6.94) ÷ 27.92 + 65.99 = ?

  1. ((a))

    61

  2. ((b))

    66

  3. ((c))

    76

  4. ((d))

    71

  5. ((e))

    81

Show Answer
Answer: ((d))

71

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

(55.89 + 11.94 × 6.94) ÷ 27.92 + 65.99 = ?

⇒ (56 + 12 × 7) ÷ 28 + 66 = ?

⇒ (56 + 84) ÷ 28 + 66 = ?

⇒ 140 ÷ 28 + 66 = ?

⇒ 5 + 66 = ?

∴ ? = 71

75

What approximate value should come in the place of question mark (?) in the following question?

689.09 – [23.982 – (122.98 + 156.97) ÷ 4.92] = ?2

  1. ((a))

    13

  2. ((b))

    17

  3. ((c))

    23

  4. ((d))

    9

  5. ((e))

    7

Show Answer
Answer: ((a))

13

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

689.09 – [23.982 – (122.98 + 156.97) ÷ 4.92] = ?2

⇒ 689 – [242 – (123 + 157) ÷ 5] = ?2

⇒ 689 – [242 – 280 ÷ 5] = ?2

⇒ 689 – [242 – 56] = ?2

⇒ 689 – [576 – 56] = ?2

⇒ 689 – 520 = ?2

∴ 13 = ?

76

What approximate value should come in the place of question mark (?) in the following question?

(117.98 + 60.92 × 1.99) ÷ 47.99 × 4.93 = ?

  1. ((a))

    20

  2. ((b))

    30

  3. ((c))

    45

  4. ((d))

    50

  5. ((e))

    25

Show Answer
Answer: ((e))

25

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

(117.98 + 60.92 × 1.99) ÷ 47.99 × 4.93 = ? 

⇒ (118 + 61 × 2) ÷ 48 × 5 = ? 

⇒ (118 + 122) ÷ 48 × 5 = ? 

⇒ 240 ÷ 48 × 5 = ? 

⇒ 5 × 5 = ?

∴ ? = 25

77

What approximate value should come in the place of question mark (?) in the following question?

√255.96 × 1.985 ÷ 7.983 × √4095.96 = ? × 63.94

  1. ((a))

    6

  2. ((b))

    8

  3. ((c))

    1

  4. ((d))

    16

  5. ((e))

    11

Show Answer
Answer: ((c))

1

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

√255.96 × 1.985 ÷ 7.983 × √4095.96 = ? × 63.94

⇒ √256 × 25 ÷ 83 × √4096 = ? × 64

⇒ 16 × 32 ÷ 512 × 64 = ? × 64 

⇒ 1 × 64 = ? × 64

⇒ 1 = ?

Directions: Study the following information carefully and answer the questions.

The table below shows the difference between the number of red and blue balls in five different bags (A, B, C, D, and E). It also provides the percentage of red balls out of the total number of balls in each bag.

BagDifference (Red - Blue)Percentage of Red Balls (out of Total)
A24066.67%
B15060%
C18062.5%
D21075%
E16057.14%

 

Note: For each bag, the total number of balls is the sum of red and blue balls only.

78

The total number of balls in Bag F is 14.28% less than the total number of balls in Bag A and Bag B combined. The ratio of Red to Blue balls in Bag F is 5:2. Find the difference between the number of red balls in Bag E and the number of blue balls in Bag F.

  1. ((a))

    280

  2. ((b))

    190

  3. ((c))

    260

  4. ((d))

    250

  5. ((e))

    340

Show Answer
Answer: ((a))

280

General Solution:

BagPercentage of Red Balls (Fraction)Total Parts (Red + Blue)Difference in Parts (Red - Blue)Value of 1 PartRed BallsBlue Balls
A66.67% = 32​Let total parts be 3. Red = 2 parts, Blue = 1 part.2−1=1240÷1=2402×240=4801×240=240
B60% = 53​Let total parts be 5. Red = 3 parts, Blue = 2 parts.3−2=1150÷1=1503×150=4502×150=300
C62.5% = 85​Let total parts be 8. Red = 5 parts, Blue = 3 parts.5−3=2180÷2=905×90=4503×90=270
D75% = 43​Let total parts be 4. Red = 3 parts, Blue = 1 part.3−1=2210÷2=1053×105=3151×105=105
E57.14% = 74​Let total parts be 7. Red = 4 parts, Blue = 3 parts.4−3=1160÷1=1604×160=6403×160=480

 

Calculations:

From table: Bag A total = 480 + 240 = 720; Bag B total = 450 + 300 = 750

⇒ A + B = 1470

Bag F total = 14.28% less than 1470 ≈ (1 − 1/7) × 1470 = (6/7) × 1470 = 1260

In F, Red : Blue = 5 : 2 (7 parts) ⇒ 1 part = 1260 ÷ 7 = 180

⇒ Blue(F) = 2 × 180 = 360

Red(E) from table = 640

Required difference = Red(E) − Blue(F) = 640 − 360 = 280

Hence, the correct answer is 280.

79

Find the difference between the average number of red balls in Bags B and C, and the average number of blue balls in Bags A and E.

  1. ((a))

    40

  2. ((b))

    70

  3. ((c))

    80

  4. ((d))

    90

  5. ((e))

    60

Show Answer
Answer: ((d))

90

General Solution:

BagPercentage of Red Balls (Fraction)Total Parts (Red + Blue)Difference in Parts (Red - Blue)Value of 1 PartRed BallsBlue Balls
A66.67% = 2/3​Let total parts be 3. Red = 2 parts, Blue = 1 part.2−1=1240÷1=2402×240=4801×240=240
B60% = 3/5​Let total parts be 5. Red = 3 parts, Blue = 2 parts.3−2=1150÷1=1503×150=4502×150=300
C62.5% = 5/8​Let total parts be 8. Red = 5 parts, Blue = 3 parts.5−3=2180÷2=905×90=4503×90=270
D75% = 3/4​Let total parts be 4. Red = 3 parts, Blue = 1 part.3−1=2210÷2=1053×105=3151×105=105
E57.14% = 4/7​Let total parts be 7. Red = 4 parts, Blue = 3 parts.4−3=1160÷1=1604×160=6403×160=480

 

Calculations:

From the table values

Bag B → Red = 450, Blue = 300

Bag C → Red = 450, Blue = 270

Bag A → Red = 480, Blue = 240

Bag E → Red = 640, Blue = 480

Average number of red balls (B and C)

⇒ (450 + 450) ÷ 2

⇒ 900 ÷ 2

⇒ 450

Average number of blue balls (A and E)

⇒ (240 + 480) ÷ 2

⇒ 720 ÷ 2

⇒ 360

Required difference

⇒ 450 − 360 = 90

Hence, the correct answer is 90.

80

If 30% of the blue balls from Bag E are transferred to Bag B, find the new percentage of red balls in Bag B. (approximate value)

  1. ((a))

    55.4%

  2. ((b))

    58.7%

  3. ((c))

    52.6%

  4. ((d))

    50.3%

  5. ((e))

    None of these

Show Answer
Answer: ((d))

50.3%

General Solution:

BagPercentage of Red Balls (Fraction)Total Parts (Red + Blue)Difference in Parts (Red - Blue)Value of 1 PartRed BallsBlue Balls
A66.67% = 2/3​Let total parts be 3. Red = 2 parts, Blue = 1 part.2−1=1240÷1=2402×240=4801×240=240
B60% = 3/5​Let total parts be 5. Red = 3 parts, Blue = 2 parts.3−2=1150÷1=1503×150=4502×150=300
C62.5% = 5/8​Let total parts be 8. Red = 5 parts, Blue = 3 parts.5−3=2180÷2=905×90=4503×90=270
D75% = 3/4​Let total parts be 4. Red = 3 parts, Blue = 1 part.3−1=2210÷2=1053×105=3151×105=105
E57.14% = 4/7​Let total parts be 7. Red = 4 parts, Blue = 3 parts.4−3=1160÷1=1604×160=6403×160=480

 

Calculations:

⇒ 30% of blue balls in E = 30% × 480 = 144

⇒ New blue in B = 300 + 144 = 444

⇒ Total in B = 450 (red) + 444 (blue) = 894

⇒ % red = (450 ÷ 894) × 100 ≈ 50.3356% ≈ 50.3%

Hence, the correct answer is 50.3%.

81

If the number of red balls in Bag C is increased by 20% and the number of blue balls is decreased by 10%, find the new ratio of red balls to blue balls in Bag C.

  1. ((a))

    14:11

  2. ((b))

    7:3

  3. ((c))

    18:7

  4. ((d))

    20:9

  5. ((e))

    None of these

Show Answer
Answer: ((d))

20:9

General Solution:

BagPercentage of Red Balls (Fraction)Total Parts (Red + Blue)Difference in Parts (Red - Blue)Value of 1 PartRed BallsBlue Balls
A66.67% = 2/3​Let total parts be 3. Red = 2 parts, Blue = 1 part.2−1=1240÷1=2402×240=4801×240=240
B60% = 3/5​Let total parts be 5. Red = 3 parts, Blue = 2 parts.3−2=1150÷1=1503×150=4502×150=300
C62.5% = 5/8​Let total parts be 8. Red = 5 parts, Blue = 3 parts.5−3=2180÷2=905×90=4503×90=270
D75% = 3/4​Let total parts be 4. Red = 3 parts, Blue = 1 part.3−1=2210÷2=1053×105=3151×105=105
E57.14% = 4/7​Let total parts be 7. Red = 4 parts, Blue = 3 parts.4−3=1160÷1=1604×160=6403×160=480

 

Calculations:

We already calculated for Bag C:

Red = 450

Blue = 270

Now apply changes:

Red increased by 20% ⇒ 450 × 1.20 = 540

Blue decreased by 10% ⇒ 270 × 0.90 = 243

So new ratio = 540 : 243

Simplify:

⇒ Divide both by 27

540 ÷ 27 = 20

243 ÷ 27 = 9

New ratio = 20 : 9

Hence, the correct answer is 20:9.

82

Find the total number of blue balls in Bags A, C, and E together.

  1. ((a))

    990

  2. ((b))

    980

  3. ((c))

    1000

  4. ((d))

    1010

  5. ((e))

    970

Show Answer
Answer: ((a))

990

General Solution:

BagPercentage of Red Balls (Fraction)Total Parts (Red + Blue)Difference in Parts (Red - Blue)Value of 1 PartRed BallsBlue Balls
A66.67% = 2/3​Let total parts be 3. Red = 2 parts, Blue = 1 part.2−1=1240÷1=2402×240=4801×240=240
B60% = 3/5​Let total parts be 5. Red = 3 parts, Blue = 2 parts.3−2=1150÷1=1503×150=4502×150=300
C62.5% = 5/8​Let total parts be 8. Red = 5 parts, Blue = 3 parts.5−3=2180÷2=905×90=4503×90=270
D75% = 3/4​Let total parts be 4. Red = 3 parts, Blue = 1 part.3−1=2210÷2=1053×105=3151×105=105
E57.14% = 4/7​Let total parts be 7. Red = 4 parts, Blue = 3 parts.4−3=1160÷1=1604×160=6403×160=480

 

Calculations:

We are asked: Find the total number of blue balls in Bags A, C, and E together.

From the General Solution Table given:

Bag A → Blue = 240

Bag C → Blue = 270

Bag E → Blue = 480

Now, total = 240 + 270 + 480 = 990

Hence, the correct answer is 990.

83

A piece of work is completed by 15 men and 10 women in 30 days. The same piece of work is completed by 10 men and 20 women in 20 days. Find the time taken by 6 men and 4 women to complete the one third of the total work?

  1. ((a))

    75 days

  2. ((b))

    45 days

  3. ((c))

    25 days

  4. ((d))

    20 days

  5. ((e))

    30 days

Show Answer
Answer: ((c))

25 days

Shortcut Trick

Work Equivalence: (15M + 10W) × 30 = (10M + 20W) × 20

⇒ 3(15M + 10W) = 2(10M + 20W) ⇒ 45M + 30W = 20M + 40W ⇒ 25M = 10W ⇒ 5M = 2W

Total Work = (15M + 10W) × 30 = (15M + 25M) × 30 = 40M × 30 = 1200M units

One-third Work = 1200M ÷ 3 = 400M units

Efficiency of (6M + 4W) = 6M + 10M = 16M

Time = 400M ÷ 16M = 25 days

∴ The correct answer is 25 days.

Alternate Method

Given: Case 1: 15 men and 10 women in 30 days. Case 2: 10 men and 20 women in 20 days. Required: Time for 6 men and 4 women for 1/3 work.

Formula Used: Total Work = (Number of workers × Efficiency) × Time

⇒ (15M + 10W) × 30 = (10M + 20W) × 20

⇒ 450M + 300W = 200M + 400W

⇒ 250M = 100W ⇒ 1W = 2.5M

⇒ Total Work = (15M + 10 × 2.5M) × 30 = (15M + 25M) × 30 = 40M × 30 = 1200M

⇒ Target Work = 1200M ÷ 3 = 400M

⇒ Efficiency of Group 3 = 6M + 4W = 6M + 4(2.5M) = 6M + 10M = 16M

⇒ Required Time = 400M ÷ 16M = 25 days

∴ The correct answer is 25 days.

Additional Information

Work-Efficiency Relation

Total work is the product of the number of people, their individual efficiencies, and the time taken (W = n × e × t).

MDH Rule

For comparing two work scenarios: (M1D1H1)/W1 = (M2D2H2)/W2.

Man-Woman Efficiency

When multiple types of workers are involved, always equate the total work equations to find the ratio of their efficiencies.

84

A certain quantity of a mixture of milk and water are in the ratio of 3: 2 respectively.If 25 litres of mixture is taken out and replaced with 7 litres of water, then the ratio of milk and water becomes 1: 1. Find the initial quantity of mixture.

  1. ((a))

    78 litres

  2. ((b))

    90 litres

  3. ((c))

    60 litres

  4. ((d))

    72 litres

  5. ((e))

    84 litres

Show Answer
Answer: ((c))

60 litres

Shortcut Trick

Ratio of Milk : Water initially = 3 : 2. After removing 25 L, ratio remains 3 : 2.

Final ratio = 1 : 1. To equate milk (3 units), final ratio becomes 3 : 3.

Water increase = 3 − 2 = 1 unit. Given 1 unit = 7 litres.

Quantity after removal = (3 + 2) × 7 = 35 litres.

Initial quantity = 35 + 25 = 60 litres.

∴ The correct answer is 60 litres.

Alternate Method

Given: Initial ratio 3 : 2. Removal = 25 L. Addition = 7 L Water. Final ratio 1 : 1.

Let the quantities of Milk and Water after removing 25 litres be 3x and 2x respectively.

⇒ According to question: 3x / (2x + 7) = 1 / 1

⇒ 3x = 2x + 7

⇒ x = 7

⇒ Mixture after removal = 3x + 2x = 5x = 5 × 7 = 35 litres

⇒ Initial quantity = 35 + 25 = 60 litres

∴ The correct answer is 60 litres.

Additional Information

Mixture Property

When a portion of a mixture is removed, the ratio of the ingredients in the remaining mixture remains the same as the initial ratio.

Replacement Method

If Milk : Water is a : b and x litres of mixture is replaced by x litres of water, the final ratio changes, but the amount of milk removed is (a/(a+b)) × x.

Alligation Rule

Quantity of Cheaper / Quantity of Dearer = (CP of Dearer − Mean Price) / (Mean Price − CP of Cheaper).

85

The lateral surface area of the cube is 676 cm2 . If the side of the cube is 4 cm more than the height of the cylinder whose volume is 972 cm3. Find the curved surface area of the cylinder.

(use π = 3)

  1. ((a))

    361 cm2

  2. ((b))

    324 cm2

  3. ((c))

    289 cm2

  4. ((d))

    144 cm2

  5. ((e))

    400 cm2

Show Answer
Answer: ((b))

324 cm2

Shortcut Trick

Lateral Surface Area (LSA) of cube = 4a2 = 676 ⇒ a2 = 169 ⇒ Side (a) = 13 cm.

Height of cylinder (h) = Side − 4 = 13 − 4 = 9 cm.

Volume of cylinder = πr2h = 3 × r2 × 9 = 972 ⇒ 27r2 = 972 ⇒ r2 = 36 ⇒ Radius (r) = 6 cm.

Curved Surface Area (CSA) = 2πrh = 2 × 3 × 6 × 9 = 324 cm2.

∴ The correct answer is 324 cm2.

Alternate Method

Given: LSA of cube = 676 cm2, Cylinder Volume = 972 cm3, π = 3.

Formula Used: LSA = 4a2; Volume = πr2h; CSA = 2πrh.

⇒ 4 × a2 = 676

⇒ a2 = 169 ⇒ a = √169 = 13 cm

⇒ Height of cylinder (h) = a − 4 = 13 − 4 = 9 cm

⇒ πr2h = 972

⇒ 3 × r2 × 9 = 972

⇒ 27 × r2 = 972 ⇒ r2 = 36 ⇒ r = 6 cm

⇒ Curved Surface Area = 2 × 3 × 6 × 9

⇒ CSA = 324 cm2

∴ The correct answer is 324 cm2.

Additional Information

Cube Mensuration Formulas

Total Surface Area (TSA) = 6a2 and Volume = a3, where 'a' is the side length.

Cylinder Mensuration Formulas

Total Surface Area (TSA) = 2πr(r + h) and Volume = πr2h.

Relationship Tip

CSA of a cylinder is also equal to (Perimeter of base × height) = 2πrh.

86

The total time taken by the boat to cover 108 km upstream and 114 km downstream in 18 hours. The speed of the boat and the speed of the stream is x + 4 km and x – 5 km/hr respectively. Find the speed of the stream.

  1. ((a))

    7 km/hr

  2. ((b))

    5 km/hr

  3. ((c))

    3 km/hr

  4. ((d))

    4 km/hr

  5. ((e))

    6 km/hr

Show Answer
Answer: ((b))

5 km/hr

Shortcut Trick

Upstream speed (U) = (x + 4) − (x − 5) = 9 km/hr.

Downstream speed (D) = (x + 4) + (x − 5) = 2x − 1 km/hr.

Upstream time = 108 ÷ 9 = 12 hours.

Downstream time = 18 − 12 = 6 hours.

Downstream speed (D) = 114 ÷ 6 = 19 km/hr ⇒ 2x − 1 = 19 ⇒ x = 10.

Speed of stream = x − 5 = 10 − 5 = 5 km/hr.

∴ The correct answer is 5 km/hr.

Alternate Method

Given:

Speed of boat in still water (u) = x + 4 km/hr

Speed of stream (v) = x − 5 km/hr

Formula Used:

Upstream Speed = u − v | Downstream Speed = u + v | Time = Distance ÷ Speed

Calculations:

⇒ Upstream Speed = (x + 4) − (x − 5) = 9 km/hr

⇒ Downstream Speed = (x + 4) + (x − 5) = (2x − 1) km/hr

⇒ Total Time = Upstream Time + Downstream Time

⇒ 18 = 108 ÷ 9 + 114 ÷ (2x − 1)

⇒ 18 = 12 + 114 ÷ (2x − 1)

⇒ 6 = 114 ÷ (2x − 1)

⇒ 2x − 1 = 114 ÷ 6 = 19

⇒ 2x = 20 ⇒ x = 10

⇒ Speed of stream = x − 5 = 10 − 5 = 5 km/hr

∴ The correct answer is 5 km/hr.

Additional Information

Upstream and Downstream Basics

When a boat moves against the current, it is upstream (u − v). When it moves with the current, it is downstream (u + v).

Average Speed of Boat

Average Speed = (Upstream Speed × Downstream Speed) ÷ Speed of Boat in Still Water (when distances are equal).

Speed Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

87

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x2 + 11x − 80 = 0

II. y2 − 27y + 110 = 0

  1. ((a))

    x > y

  2. ((b))

    x < y

  3. ((c))

    x ≥ y

  4. ((d))

    x ≤ y

  5. ((e))

    x = y or relationship between x and y cannot be established.

Show Answer
Answer: ((d))

x ≤ y

I. x2 + 11x − 80 = 0

⇒ x2 + 16x − 5x − 80 = 0

⇒ (x + 16), (x − 5) = 0

x = − 16, 5

II. y2 − 27y + 110 = 0

⇒ (y − 22)(y − 5) = 0

 y = 22, 5

Value of xValue of yRelation
-165x < y
-1622x < y
55x = y
522x < y

∴ x ≤ y

88

In these question, two equations (I) and (II) are given. You have to solve both the equations and answer accordingly:

(I) 2x2 + 15x + 28 = 0

(II) 3y2 + 11y + 6 = 0

  1. ((a))

    If x > y

  2. ((b))

    If  x ≥ y

  3. ((c))

    If y > x

  4. ((d))

    If y ≥ x

  5. ((e))

    x = y or the relationship between x and y cannot be established.

Show Answer
Answer: ((c))

If y > x

Calculation:

2x2 + 15x + 28 = 0

⇒ 2x2 + 8x + 7x + 28 = 0

⇒ 2x(x + 4) + 7(x + 4)

⇒ x = -4, -7/2

3y2 + 11y + 6 = 0

⇒ 3y2 + 9y + 2y + 6 = 0

⇒ 3y(y + 3) + 2(y + 3)

⇒ Y = -3, -2/3

Comparison between X and Y (via tabulation):

Value of xValue of yRelation
-4-3x < y
-4-2/3x < y
-7/2-3x < y
-7/2-2/3x < y

∴ x < y

89

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x2 + 28x + 147 = 0

II. y2 – 15y – 154 = 0

  1. ((a))

    x > y

  2. ((b))

    x ≥ y

  3. ((c))

    y > x

  4. ((d))

    y ≥ x

  5. ((e))

    x = y or relationship between x and y cannot be established.

Show Answer
Answer: ((d))

y ≥ x

According to given equations

I. x2 + 28x + 147 = 0

⇒ x2 + 21x + 7x + 147 = 0

⇒ x(x + 21) + 7(x + 2) = 0

⇒ (x + 21) (x + 7) = 0

⇒ x = -21, -7

II. y2 – 15y – 154 = 0 

⇒ y2 – 22y + 7y – 154 = 0

⇒ y(y – 22) + 7(y – 22) = 0

⇒ (y – 22) (y + 7) = 0

⇒ y = 22, -7

Comparison between x and y (via Tabulation):

xyRelation
-2122x<y
-21-7x<y
-722x<y
-7-7x=y

 ∴ y ≥ x

90

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x2 –  15x + 44 = 0

II. 3y2 –  22y + 35 = 0

  1. ((a))

    x > y

  2. ((b))

    x ≥ y

  3. ((c))

    y > x

  4. ((d))

    y ≥ x

  5. ((e))

    x = y or relationship between x and y cannot be established.

Show Answer
Answer: ((e))

x = y or relationship between x and y cannot be established.

According to given equations

I. x2 – 15x + 44 = 0

⇒ x2 – 11x – 4x + 44 = 0

⇒ x(x – 11) – 4(x – 11) = 0

⇒ (x – 4) (x – 11) = 0

⇒ x = 11, 4

II. 3y2 – 22y + 35 = 0

⇒ 3y2 – 15y – 7y + 35 = 0

⇒ 3y(y – 5) – 7(y – 5) = 0

⇒ (y – 5) (3y – 7) = 0

⇒ y = 7/3, 5

Comparison between x and y (via Tabulation):

xyRelation
117/3x > y
115x > y
47/3x > y
45x < y
<br>

∴ The relationship between x and y cannot be established.

91

The average weight of 50 people group is 48kg. There are new 10 peoples added in the group of average weight 45kg. From original group, there are 5 peoples of average weight 50kg are removed. Find the approximate average weight of newly formed group.

  1. ((a))

    50 kg

  2. ((b))

    47 kg

  3. ((c))

    40 kg

  4. ((d))

    51 kg

  5. ((e))

    43 kg

Show Answer
Answer: ((b))

47 kg

Shortcut Trick

Net change in weight = (10 × (45 − 48)) − (5 × (50 − 48))

Net change = −30 − 10 = −40 kg

New total people = 50 + 10 − 5 = 55

New Average = 48 + (−40 ÷ 55) ≈ 48 − 0.72 = 47.28 kg

∴ The correct answer is 47 kg.

Alternate Method

Given: Initial 50 people (avg 48kg), Added 10 people (avg 45kg), Removed 5 people (avg 50kg).

Formula: Average = Total Weight ÷ Number of People

⇒ Total Weight = (50 × 48) + (10 × 45) − (5 × 50)

⇒ Total Weight = 2400 + 450 − 250 = 2600 kg

⇒ Total Number of People = 50 + 10 − 5 = 55

⇒ New Average = 2600 ÷ 55 = 47.2727... kg

⇒ Approximate Average ≈ 47 kg

∴ The correct answer is 47 kg.

Additional Information

Weighted Average Formula

Average = (n1x1 + n2x2 − n3x3) ÷ (n1 + n2 − n3) where x represents the average and n represents number of observations.

Deviation Method for Averages

Net Deviation = ∑(Individual Values − Assumed Average). New Average = Assumed Average + (Net Deviation ÷ Total Number).

92

A train covers a distance of 450 km at an uniform speed. Had the speed been 10 kmph more, it would have taken 30 minutes less for the journey. How much time does this train take to cover 3/5th of the journey?

  1. ((a))

    2 hours

  2. ((b))

    3 hours

  3. ((c))

    5 hours

  4. ((d))

    4 hours

  5. ((e))

    6 hours

Show Answer
Answer: ((b))

3 hours

Shortcut Trick

Let original speed be S kmph. Using the product of speed formula: Distance = [S1 × S2 / (S2 − S1)] × Time Difference.

450 = [S × (S + 10) / 10] × (30/60) ⇒ 450 = [S(S + 10) / 10] × 1/2.

S(S + 10) = 9000 ⇒ S = 90 kmph (as 90 × 100 = 9000).

Time for 3/5th journey = (3/5 × 450) ÷ 90 = 270 ÷ 90 = 3 hr.

∴ The correct answer is 3 hr.

Alternate Method

Given: Total distance = 450 km, Speed increase = 10 kmph, Time saved = 30 mins = 0.5 hr.

Formula Used: Time = Distance / Speed

⇒ (450 / S) − [450 / (S + 10)] = 1/2

⇒ 450 [ (S + 10 − S) / (S(S + 10)) ] = 1/2

⇒ 450 [ 10 / (S2 + 10S) ] = 1/2

⇒ 4500 × 2 = S2 + 10S

⇒ S2 + 10S − 9000 = 0

⇒ S2 + 100S − 90S − 9000 = 0 ⇒ (S + 100)(S − 90) = 0

⇒ S = 90 kmph (Speed cannot be negative)

⇒ 3/5th Distance = 3/5 × 450 = 270 km

⇒ Time required = 270 / 90 = 3 hr

∴ The correct answer is 3 hr.

Additional Information

Speed-Time Inversely Proportional

For a constant distance, speed is inversely proportional to time (S1/S2 = T2/T1).

Distance Formula for Speed Change

Distance = [v1v2 / |v1−v2|] × Δt, where Δt is the difference in time taken at speeds v1 and v2.

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal halves of a journey with speeds x and y, it is 2xy/(x+y).

The line graph shows the number of Tv sold and number of differences between number of Tv and cell phone sold in five different shops [A, B, C, D and E]. Number of Tv sold is more than the number of cell phone in each shop.

93

If the selling price of each TV is ₹15,000 and each Cell phone is ₹8,000, then what is the total revenue difference between Shop C and Shop B?

  1. ((a))

    1680000

  2. ((b))

    145000

  3. ((c))

    147000

  4. ((d))

    194500

  5. ((e))

    254000

Show Answer
Answer: ((a))

1680000

Common Calculation

Number of TV sold in shop A is 120.

Difference between number of TV and cell phone sold in shop A is 40.

Number of TV sold in each shop is more than number of cell phone sold.

So, Number of cell phone sold in shop A is 120 – 40 = 80.

Similarly, we can calculate others shops values also.

ShopNumber of TV soldNumber of Cell phone sold
A12080
B160100
C240160
D10080
E180120

Calculation

Shop C revenue = (240 × 15000) + (160 × 8000) = 48,80,000

Shop B revenue = (160 × 15000) + (100 × 8000) = 32,00,000

Difference = 4880000 - 3200000 = 16,80,000

94

Average number of TVs sold across all 5 shops is what percent more than the average number of Cell phones sold across all 5 shops?

  1. ((a))

    48%

  2. ((b))

    62%

  3. ((c))

    55%

  4. ((d))

    39%

  5. ((e))

    28%

Show Answer
Answer: ((a))

48%

Common Calculation

Number of TV sold in shop A is 120.

Difference between number of TV and cell phone sold in shop A is 40.

Number of TV sold in each shop is more than number of cell phone sold.

So, Number of cell phone sold in shop A is 120 – 40 = 80.

Similarly, we can calculate others shops values also.

ShopNumber of TV soldNumber of Cell phone sold
A12080
B160100
C240160
D10080
E180120

Calculation

Total TVs = 800 → Avg = 160

Total Cell phones = 540 → Avg = 108

% more = [(160 - 108)/108] × 100 ≈ 48.15%

95

What is the ratio of total number of TVs sold in Shops A and C together to the total number of Cell phones sold in Shops B and D together?

  1. ((a))

    2:1

  2. ((b))

    3:2

  3. ((c))

    5:4

  4. ((d))

    7:9

  5. ((e))

    9:7

Show Answer
Answer: ((a))

2:1

Common Calculation

Number of TV sold in shop A is 120.

Difference between number of TV and cell phone sold in shop A is 40.

Number of TV sold in each shop is more than number of cell phone sold.

So, Number of cell phone sold in shop A is 120 – 40 = 80.

Similarly, we can calculate others shops values also.

ShopNumber of TV soldNumber of Cell phone sold
A12080
B160100
C240160
D10080
E180120

Calculation

TVs in A + C = 120 + 240 = 360

Cell phones in B + D = 100 + 80 = 180

Ratio = 360 : 180 = 2 : 1

96

By what percentage is the total number of items (TVs + Cell phones) sold in Shop E greater than that in Shop A?

  1. ((a))

    50%

  2. ((b))

    48%

  3. ((c))

    64%

  4. ((d))

    28%

  5. ((e))

    55%

Show Answer
Answer: ((a))

50%

Common Calculation

Number of TV sold in shop A is 120.

Difference between number of TV and cell phone sold in shop A is 40.

Number of TV sold in each shop is more than number of cell phone sold.

So, Number of cell phone sold in shop A is 120 – 40 = 80.

Similarly, we can calculate others shops values also.

ShopNumber of TV soldNumber of Cell phone sold
A12080
B160100
C240160
D10080
E180120

Calculation

Shop A total = 120 + 80 = 200

Shop E total = 180 + 120 = 300

Increase = 100

% Increase = (100/200) × 100 = 50%

97

If 25% of TVs sold in Shop D were returned and 20% of Cell phones sold in Shop A were defective, then what is the ratio of remaining good items in Shop D to those in Shop A?

  1. ((a))

    155:184

  2. ((b))

    162:147

  3. ((c))

    137:157

  4. ((d))

    121:159

  5. ((e))

    161:137

Show Answer
Answer: ((a))

155:184

Common Calculation

Number of TV sold in shop A is 120.

Difference between number of TV and cell phone sold in shop A is 40.

Number of TV sold in each shop is more than number of cell phone sold.

So, Number of cell phone sold in shop A is 120 – 40 = 80.

Similarly, we can calculate others shops values also.

ShopNumber of TV soldNumber of Cell phone sold
A12080
B160100
C240160
D10080
E180120

Calculation

Shop D: TVs good = [100 × 75/100] =75, Cell phones = 80 → Total = 155

Shop A: TVs = 120, Cell phones good = [80 × 80/100] = 64 → Total = 184

Ratio = 155 : 184

98

Laxmi borrowed certain sum from Raj. Simple interest on that sum for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

  1. ((a))

    Rs 1750

  2. ((b))

    Rs 2000

  3. ((c))

    Rs 1500

  4. ((d))

    Rs 1800

  5. ((e))

    None of these

Show Answer
Answer: ((a))

Rs 1750

Shortcut Trick

Compound Interest (CI) on ₹4000 at 10% for 2 years: Effective rate = 10 + 10 + (10×10)/100 = 21%.

CI = 21% of 4000 = ₹840.

Simple Interest (SI) = 1/2 × 840 = ₹420.

SI % for 3 years at 8% = 3 × 8 = 24%.

Principal = 420 ÷ 24% = 420 ÷ 0.24 = ₹1750.

∴ The correct answer is ₹1750.

Alternate Method

Given:

Compound Interest: P = ₹4000, R = 10%, T = 2 years.

Simple Interest: R = 8%, T = 3 years.

Formula Used:

CI = P[(1 + R/100)T − 1]

SI = (P × R × T) / 100

Calculations:

⇒ CI = 4000 × [(1 + 10/100)2 − 1]

⇒ CI = 4000 × [1.21 − 1] = 4000 × 0.21 = ₹840.

⇒ Given: SI = 1/2 × 840 = ₹420.

⇒ 420 = (Sum × 8 × 3) / 100

⇒ 420 = (Sum × 24) / 100

⇒ Sum = (420 × 100) / 24

⇒ Sum = ₹1750.

∴ The correct answer is ₹1750.

Additional Information

Effective Rate for Compound Interest

For 2 years, the effective rate is calculated as (x + y + xy/100)%. This helps avoid long power calculations.

Difference between CI and SI

The difference for 2 years is P(R/100)2. For 3 years, it is P(R/100)2 × (3 + R/100).

Simple Interest Property

Simple interest remains constant every year on the same principal, unlike compound interest where interest is earned on interest.

99

The present age of A and B are in the ratio 11 : 9. 2 years from now the age of A is 2/3rd of the C. If the present age of C is 34. 4 years ago the age of A is 50% of the age of D. Find the difference between the age of A 3 years ago and age of D 5 years hence.

  1. ((a))

    34

  2. ((b))

    26

  3. ((c))

    24

  4. ((d))

    30

  5. ((e))

    32

Show Answer
Answer: ((b))

26

Shortcut Trick

C present age = 34 years → C (2 yrs later) = 36 years.

A (2 yrs later) = 2/3 × 36 = 24 years → A present age = 22 years.

A (4 yrs ago) = 18 years, which is 50% of D (4 yrs ago) → D (4 yrs ago) = 36 years.

D present = 40 years. Required Difference = |(22 − 3) − (40 + 5)| = |19 − 45| = 26 years.

∴ The correct answer is 26 years.

Alternate Method

Given: Ratio A:B = 11:9 | C present = 34 | A (present + 2) = 2/3 × C (present + 2)

C (2 years hence) = 34 + 2 = 36 years

A (2 years hence) = (2/3) × 36 = 24 years

A (Present age) = 24 − 2 = 22 years

⇒ Since A:B is 11:9, 11 units = 22 → 1 unit = 2 (B = 18 years, though not needed)

A (4 years ago) = 22 − 4 = 18 years

A (4 years ago) = 50% of D (4 years ago) ⇒ 18 = 0.5 × D4_agoD (4 years ago) = 36 years

D (Present age) = 36 + 4 = 40 years

⇒ Age of A 3 years ago = 22 − 3 = 19 years

⇒ Age of D 5 years hence = 40 + 5 = 45 years

Difference = 45 − 19 = 26 years

∴ The correct answer is 26 years.

Additional Information

Ratio and Proportions in Ages

When the ratio of ages at two different time points is given, the difference between the ages remains constant. Use 1 unit value to find actual ages.

Percentage and Fraction conversion

50% of a value is equivalent to 1/2 of the value. If X is 50% of Y, then Y = 2 × X.

Age Difference Consistency

The difference between the ages of two people always remains the same regardless of how many years pass or have passed.

100

In a town 60% of the population is males and remaining are females, out of the males 40% are literate and remaining are illiterate, out of 25% female are literate and remaining are illiterate. If total number of literate population is 102000 what is the population of the town ?

  1. ((a))

     280000

  2. ((b))

     300000

  3. ((c))

     400000

  4. ((d))

     216000

  5. ((e))

     288000

Show Answer
Answer: ((b))

 300000

Shortcut Trick

Assume total population = 100 units.

Males = 60; Females = 40.

Literate Males = 40% of 60 = 24; Literate Females = 25% of 40 = 10.

Total Literate = 24 + 10 = 34 units → 102000.

1 unit = 3000 ∴ 100 units = 300000.

∴ The correct answer is 300000.

Alternate Method

Given:

Total literate population = 102000

Calculations:

⇒ Let total population be x.

⇒ Males = 60% of x = 0.60x

⇒ Females = 40% of x = 0.40x

⇒ Literate Males = 40% of 0.60x = 0.24x

⇒ Literate Females = 25% of 0.40x = 0.10x

⇒ Total Literate = 0.24x + 0.10x = 0.34x

⇒ 0.34x = 102000

⇒ x = 102000 ÷ 0.34

⇒ x = 300000

∴ The correct answer is 300000.

Additional Information

Percentage Base Change

When calculating percentages of sub-groups, always multiply the sub-group percentage by its parent group percentage (e.g., % of Literate Males = % Literate × % Males).

Successive Percentage

If a value changes by a% and then b%, the effective change is [a + b + (ab/100)]%.

Unitary Method in Percentage

If p% of a total is known (V), then the total 100% is calculated as (V ÷ p) × 100.

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