Official Paper

RRB Clerk Prelims Memory Based Paper (Held on: 19 September 2020 Shift 2) (Previous Year Paper)

80 questions · 45 minutes · with answers · free

Reasoning (40 questions)

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: D > F ≥ G ≥ H; H ≥ I = J

Conclusions

I. J = F

II. F > J

((a))
Only II is True
((b))
Only I is True
((c))
Both I and II are True
((d))
Either I or II is True
((e))
None is true

Show Answer

Answer: ((d))

Either I or II is True

Given statements: D > F ≥ G ≥ H; H ≥ I = J

On combining: D > F ≥ G ≥ H ≥ I = J

Conclusions:

I. J = F → False (as F ≥ G ≥ H ≥ I = J → J ≤ F)

II. F > J → False (as F ≥ G ≥ H ≥ I = J → F ≥ J)

Therefore, conclusion I and II forms a complementary pair.

Hence, Either I or II is True.

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:

L = G ≥ H = N; C > K ≥ Q = N

Conclusions:

K ≥ L

C ≥ G

((a))
Only I is True
((b))
Only II is True
((c))
Both I and II are True
((d))
Either I and II is True
((e))
Neither I and II is True

Show Answer

Answer: ((e))

Neither I and II is True

Given statements: L = G ≥ H = N; C > K ≥ Q = N

Combined Statement: L = G ≥ H = N = Q ≤ K < C

Conclusions:

K ≥ L → False → as L = G ≥ H = N = Q ≤ K < C → thus clear relation between K and L cannot be determined)

C ≥ G → False → as L = G ≥ H = N = Q ≤ K < C → thus clear relation between C and G cannot be determined)

Hence, Neither I and II is True

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: P > Q = V; V < T

Conclusions:

I. Q = T

II. T > P

((a))
Only I is true
((b))
Only II is true
((c))
Either I or II is true
((d))
Neither I or II is true
((e))
Both are true

Show Answer

Answer: ((d))

Neither I or II is true

Given statements: P > Q = V; V < T

On combining: P > Q = V < T

I. Q = T → False (as Q = V < T → Q < T)

II. T > P → False (as direct relation between T and P can’t be determined)

Both conclusions are false, hence, neither is true.

Direction: In each of 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: J < G ≥ L > N < K ≤ F < T = H

Conclusions:

I. F > L

II.K < H

((a))
Only II follows
((b))
Only I follows
((c))
Both I and II follow
((d))
Either I or II follow
((e))
None follows

Show Answer

Answer: ((a))

Only II follows

Given statement: J < G ≥ L > N < K ≤ F < T = H

Conclusion:

I. F > L → False (as L > N < K ≤ F) thus clear relation between F and L cannot be determined as symbols are in reverse order.

II. K < H → True (as K ≤ F → F < T → T = H → So, K < H)

Therefore, only conclusion II follows.

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, D ≥ F ≥ E

Conclusions:

I. B > E

II.C > A

((a))
None is True
((b))
Both I and II are True
((c))
Only II is True
((d))
Only I is True
((e))
Either I or II is True

Show Answer

Answer: ((b))

Both I and II are True

Given statements: A D, D ≥ F ≥ E

Conclusions:

I. B > E → True [B = C > D ≥ F ≥ E, Hence, B > E]

II. C > A → True[AS C = B > A]

Hence, bothI& II are True.

Directions: In the question below are given two statements followed by two conclusions numbered I and II. 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. Only a few E are D.

II. Some E are N

Conclusions:

I. Some N are E

II. Some E are not D

((a))
Only conclusion I follows.
((b))
Only conclusion II follows.
((c))
Both conclusion I and II follow.
((d))
Either conclusion I or conclusion II follows.
((e))
Neither conclusion I nor conclusion II follows.

Show Answer

Answer: ((c))

Both conclusion I and II follow.

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

I. Some N are E → True( It is definite )

II. Some E are not D → True( because given only a few E are D. it means some E are definitely D and some E are not definitely D )

Hence, Both conclusions I and II follow.

Only few = some + Some not

Only few A are B means 'Some A are B' as well as 'Some A are not B'.

In the question below are given two statements followed by two conclusions numbered I and II. 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. Only a few plant is tree

II. Some tree is not leaf

Conclusions:

I. Some tree is leaf

II. Some plant is tree

((a))
Only conclusion I follows
((b))
Only conclusion II follows
((c))
Both conclusion I and II follows
((d))
Either conclusion I or II follows
((e))
Neither conclusion I nor II follows

Show Answer

Answer: ((b))

Only conclusion II follows

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

I. Some tree is leaf → False (It can be possible, but it is not definite)

II. Some plant is tree → True (It is definite)

Hence, only conclusion II follows.

Direction: In the question below are given two statements followed by two conclusions numbered I and II. 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:

Some wood is chair.

Some chairs are tables.

Conclusions:

I. Some wood is table.

II. Some tables being wood is a possibility.

((a))
None follows
((b))
Either I or II follows
((c))
Only II follows
((d))
Both I & II follow
((e))
Only I follows

Show Answer

Answer: ((c))

Only II follows

The least possible Venn diagram for the given statements is as follow:

Conclusions:

I. Some wood is table → False (it is possible but not definite.)

II. Some tables being wood is a possibility → True (it is possible.)

Thus, only conclusion II follows.

Statements:

Some fruits are flowers.

All flowers are plants.

Conclusions:

I. No fruit being plant is a possibility.

II. Some fruits are plants.

((a))
None follows
((b))
Either I or II follows
((c))
Only II follows
((d))
Both I & II follow
((e))
Only I follows

Show Answer

Answer: ((c))

Only II follows

The least possible Venn diagram for the given statements is as follow:

Conclusions:

I. No fruit being plant is a possibility → False (it is not possible.)

II. Some fruits are plants → True (it is definite.)

Thus, only conclusion II follows.

Direction: In the question below, there are two statements followed by two conclusions numbered I and II. 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:

Some Soap are Shampoo.

All Shampoo are Conditioner.

Conclusions:

I. Some Soap are Conditioner.

II. No Soap is Conditioner.

((a))
Only I follows
((b))
Only II follows
((c))
Both I and II follows
((d))
Neither I nor II follows
((e))
Either I or II follows

Show Answer

Answer: ((a))

Only I follows

The least possible Venn Diagram for the given statements will be as follows,

I. Some Soap are Conditioner → True (As some soap are shampoo and all shampoo are conditioner, some soap is definitely conditioner.)

II. No Soap is Conditioner → False (Some soap is definitely conditioner)

Hence, ‘Only I follows’ is the correct answer.

Direction: Read the following information carefully and answer the questions that follow:

A certain number of persons are sitting in a row facing north. A is sitting second from one of the ends. Four persons are sitting between B and D. There are two persons sitting between A and B. D is sitting just left of C. F sits three places away to the right of B. E sits at the extreme right end of the row. G sits to the immediate right of B. Two persons are sitting between C and E.

How many persons are sitting in the row?

((a))
12
((b))
20
((c))
14
((d))
16
((e))
18

Show Answer

Answer: ((c))

A is sitting second from one of the ends.

(Here, we will have two cases, Case 1: when A is second from the left end and Case 2: when A is second from the right end).

There are two persons sitting between A and B.

Four persons are sitting between B and D.
D is sitting just left of C.

F sits three places away to the right of B.

(Here, we can eliminate case 2 as A is already three places away to the right of B).

E sits at the extreme right end of the row.

G sits to the immediate right of B.
Two persons are sitting between C and E.

Hence, the final arrangement will be as follows:

Hence, 14 persons are sitting in the row.

Who is sitting exactly between A and D?

((a))
B
((b))
G
((c))
F
((d))
C
((e))
E

Show Answer

Answer: ((b))

A is sitting second from one of the ends.

(Here, we will have two cases, Case 1: when A is second from the left end and Case 2: when A is second from the right end).

There are two persons sitting between A and B.

Four persons are sitting between B and D.
D is sitting just left of C.

F sits three places away to the right of B.

(Here, we can eliminate case 2 as A is already three places away to the right of B).

E sits at the extreme right end of the row.

G sits to the immediate right of B.
Two persons are sitting between C and E.

Hence, the final arrangement will be as follows:

Hence, G is sitting exactly between A and D.

Who is sitting third to the left of E?

((a))
A
((b))
B
((c))
D
((d))
C
((e))
F

Show Answer

Answer: ((d))

A is sitting second from one of the ends.

(Here, we will have two cases, Case 1: when A is second from the left end and Case 2: when A is second from the right end).

There are two persons sitting between A and B.

Four persons are sitting between B and D.
D is sitting just left of C.

F sits three places away to the right of B.

(Here, we can eliminate case 2 as A is already three places away to the right of B).

E sits at the extreme right end of the row.

G sits to the immediate right of B.
Two persons are sitting between C and E.

Hence, the final arrangement will be as follows:

Hence, C is sitting third to the left of E.

What is the position of B from the left end?

((a))
Third
((b))
Fourth
((c))
Sixth
((d))
Fifth
((e))
Seventh

Show Answer

Answer: ((d))

Fifth

A is sitting second from one of the ends.

(Here, we will have two cases, Case 1: when A is second from the left end and Case 2: when A is second from the right end).

There are two persons sitting between A and B.

Four persons are sitting between B and D.
D is sitting just left of C.

F sits three places away to the right of B.

(Here, we can eliminate case 2 as A is already three places away to the right of B).

E sits at the extreme right end of the row.

G sits to the immediate right of B.
Two persons are sitting between C and E.

Hence, the final arrangement will be as follows:

Hence, the position of B from the left end is fifth.

How many persons are sitting between G and C?

((a))
Three
((b))
Two
((c))
Five
((d))
Six
((e))
Four

Show Answer

Answer: ((e))

Four

A is sitting second from one of the ends.

(Here, we will have two cases, Case 1: when A is second from the left end and Case 2: when A is second from the right end).

There are two persons sitting between A and B.

Four persons are sitting between B and D.
D is sitting just left of C.

F sits three places away to the right of B.

(Here, we can eliminate case 2 as A is already three places away to the right of B).

E sits at the extreme right end of the row.

G sits to the immediate right of B.
Two persons are sitting between C and E.

Hence, the final arrangement will be as follows:

Hence, four persons are sitting between G and C.

Directions: Study the information given below carefully and answer the questions that follow.

Seven people named A, B, C, D, E, F, and G are sitting in a row facing north but not necessarily in the same order. A sits third from one of the extreme ends. Two people sit between A and B. C sits at the immediate left of B. F sits fourth to the left of B. G sits third to the right of E. E does not sit any of the extreme ends.

Who among the following sits at the left end of the row?

((a))
G
((b))
F
((c))
D
((d))
E
((e))
A

Show Answer

Answer: ((c))

7 people: A, B, C, D, E, F, G

1) A sits third from one of the extreme ends.

2) Two people sit between A and B.

Case 1:

		A			B

Case 2:

	B			A

4) F sits fourth to the left of B.

3) C sits at the immediate left of B.

Therefore, case 2 gets eliminated.

		A		C	B

5) G sits third to the right of E.

E does not sit any of the extreme ends.

Thus, the final arrangement is as follows:

D	F	A	E	C	B	G

Hence D sits at the left end of the row.

Who is sitting in the middle of the row?

((a))
A
((b))
B
((c))
C
((d))
D
((e))
E

Show Answer

Answer: ((e))

7 people: A, B, C, D, E, F, G

1) A sits third from one of the extreme ends.

2) Two people sit between A and B.

Case 1:

		A			B

Case 2:

	B			A

4) F sits fourth to the left of B.

3) C sits at the immediate left of B.

Therefore, case 2 gets eliminated.

		A		C	B

5) G sits third to the right of E.

E does not sit any of the extreme ends.

Thus, the final arrangement is as follows:

D	F	A	E	C	B	G

Hence E is sitting in the middle of the row.

What is the position of F with respect to C?

((a))
Third to the left
((b))
Second to the right
((c))
Immediate right
((d))
Second to the left
((e))
Fourth to the right

Show Answer

Answer: ((a))

Third to the left

7 people: A, B, C, D, E, F, G

1) A sits third from one of the extreme ends.

2) Two people sit between A and B.

Case 1:

		A			B

Case 2:

	B			A

4) F sits fourth to the left of B.

3) C sits at the immediate left of B.

Therefore, case 2 gets eliminated.

		A		C	B

5) G sits third to the right of E.

E does not sit any of the extreme ends.

Thus, the final arrangement is as follows:

D	F	A	E	C	B	G

Hence F sits third to the left of C.

Who is sitting fourth to the right of A?

((a))
D
((b))
E
((c))
F
((d))
G
((e))
C

Show Answer

Answer: ((d))

7 people: A, B, C, D, E, F, G

1) A sits third from one of the extreme ends.

2) Two people sit between A and B.

Case 1:

		A			B

Case 2:

	B			A

4) F sits fourth to the left of B.

3) C sits at the immediate left of B.

Therefore, case 2 gets eliminated.

		A		C	B

5) G sits third to the right of E.

E does not sit any of the extreme ends.

Thus, the final arrangement is as follows:

D	F	A	E	C	B	G

Hence G sits fourth to the right of A.

Who are the immediate neighbours of E?

((a))
BC
((b))
AC
((c))
DG
((d))
FG
((e))
CG

Show Answer

Answer: ((b))

7 people: A, B, C, D, E, F, G

1) A sits third from one of the extreme ends.

2) Two people sit between A and B.

Case 1:

		A			B

Case 2:

	B			A

4) F sits fourth to the left of B.

3) C sits at the immediate left of B.

Therefore, case 2 gets eliminated.

		A		C	B

5) G sits third to the right of E.

E does not sit any of the extreme ends.

Thus, the final arrangement is as follows:

D	F	A	E	C	B	G

Hence A and C are the immediate neighbours of E.

Directions: Read the following information carefully and answer the questions asked below.

Seven people, namely, A, B, C, D, E, F, and G have their interviews scheduled for a job at different times in a day. Only D has an interview scheduled before F. There are three interviews scheduled after the interview of C. There are two interviews scheduled between the interviews of A and B. Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

How many interview(s) are scheduled after the interview of A?

((a))
One
((b))
Two
((c))
Three
((d))
Four
((e))
Five

Show Answer

Answer: ((d))

Four

7 people: A, B, C, D, E, F, and G

1) Only D has an interview scheduled before F.

2) There are three interviews scheduled after the interview of C.

In the below table, the person at the top has the earliest scheduled interview followed by the ones after him.

D
F

C

3) There are two interviews scheduled between the interviews of A and B.

Case 1:

D
F
A
C

B

Case 2:

D
F
B
C

A

4)Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

Therefore, case 2 gets eliminated.

Thus, the final order is:

D
F
A
C
E
B
G

Hence four interviews are scheduled after the interview of A.

Whose interview is scheduled at the last?

((a))
A
((b))
C
((c))
B
((d))
G
((e))
D

Show Answer

Answer: ((d))

7 people: A, B, C, D, E, F, and G

1) Only D has an interview scheduled before F.

2) There are three interviews scheduled after the interview of C.

In the below table, the person at the top has the earliest scheduled interview followed by the ones after him.

D
F

C

3) There are two interviews scheduled between the interviews of A and B.

Case 1:

D
F
A
C

B

Case 2:

D
F
B
C

A

4)Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

Therefore, case 2 gets eliminated.

Thus, the final order is:

D
F
A
C
E
B
G

Hence the interview of G is scheduled at the last.

The number of interviews scheduled between the interviews of F and B is ________

((a))
One
((b))
Two
((c))
Three
((d))
Four
((e))
Five

Show Answer

Answer: ((c))

Three

7 people: A, B, C, D, E, F, and G

1) Only D has an interview scheduled before F.

2) There are three interviews scheduled after the interview of C.

In the below table, the person at the top has the earliest scheduled interview followed by the ones after him.

D
F

C

3) There are two interviews scheduled between the interviews of A and B.

Case 1:

D
F
A
C

B

Case 2:

D
F
B
C

A

4)Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

Therefore, case 2 gets eliminated.

Thus, the final order is:

D
F
A
C
E
B
G

Hence the number of interviews scheduled between the interviews of F and B is three.

Whose interview is scheduled immediately before the interview of C?

((a))
A
((b))
B
((c))
D
((d))
E
((e))
F

Show Answer

Answer: ((a))

7 people: A, B, C, D, E, F, and G

1) Only D has an interview scheduled before F.

2) There are three interviews scheduled after the interview of C.

In the below table, the person at the top has the earliest scheduled interview followed by the ones after him.

D
F

C

3) There are two interviews scheduled between the interviews of A and B.

Case 1:

D
F
A
C

B

Case 2:

D
F
B
C

A

4)Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

Therefore, case 2 gets eliminated.

Thus, the final order is:

D
F
A
C
E
B
G

Hence the interview of A is scheduled immediately before the interview of C

The number of interviews before the interview of E is same as the number of interviews after the interview of ________

((a))
A
((b))
B
((c))
C
((d))
D
((e))
G

Show Answer

Answer: ((a))

7 people: A, B, C, D, E, F, and G

1) Only D has an interview scheduled before F.

2) There are three interviews scheduled after the interview of C.

In the below table, the person at the top has the earliest scheduled interview followed by the ones after him.

D
F

C

3) There are two interviews scheduled between the interviews of A and B.

Case 1:

D
F
A
C

B

Case 2:

D
F
B
C

A

4)Interview of E is not scheduled after the interview of G who has an interview immediately after that of B.

Therefore, case 2 gets eliminated.

Thus, the final order is:

D
F
A
C
E
B
G

Hence the number of interviews before the interview of E is the same as the number of interviews after the interview of A.

How many pairs of letters are there in the word “PROBLEM” each of which has as many letters between them as in the English alphabetical series in both forward and backward directions?

((a))
One
((b))
Two
((c))
Three
((d))
Four
((e))
More than Four

Show Answer

Answer: ((b))

Two

Word: PROBLEM

The alphabets are positioned as in the following order,

The given word can be represented as follows,

Backward: PL and RM

Hence, there are two such pairs.

If in the word JUNIOR all the letters are arranged alphabetically, then the position of how many letter/letters will remain unchanged?

((a))
One
((b))
Two
((c))
Three
((d))
Four
((e))
None

Show Answer

Answer: ((a))

One

Word: JUNIOR

Thus, only position of N remains unchanged.

Hence, one is the answer.

Directions: Study the following information carefully to answer the given questions:

S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £

If all the symbols in the above arrangement are replaced with digit ‘0’, then which of the following will be tenth from right end?

((a))
0
((b))
5
((c))
T
((d))
U
((e))
2

Show Answer

Answer: ((b))

Given series:

Left side S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £ Right side

If all the symbols in the above arrangement are replaced with digit ‘0’,

Left side S Y 0 1 8 O 9 W A 0 4 6 E 0 2 0 U 5 T 0 B 0 N 3 0 7 0 Right side

Tenth from right side is 5

Hence, 5 is the correct answer.

If all the vowels in the above arrangement are dropped, then how many numbers will be immediately preceded by a symbol and immediately followed by a consonant?

((a))
Three
((b))
Five
((c))
Two
((d))
One
((e))
Four

Show Answer

Answer: ((d))

One

Given series:

Left side S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £ Right side

If all the vowels in the above arrangement are dropped, then numbers that will be immediately preceded by a symbol and immediately followed by a consonant:

Required order is: Symbol → Number → Consonant

Left side S Y % 1 8 9 W & 4 6 * 2 @ 5 T # B $ N 3 © 7 £ Right side

Hence, there is only one number which is immediately preceded by a symbol and immediately followed by a consonant: @ 5 T

Four of the following five are alike in a certain way based on their positions in the above arrangement and so form a group. Which is the one that does not belong to that group?

((a))
@ T #
((b))
W 4 6
((c))
Y 1 O
((d))
$ © 7
((e))
9 & 4

Show Answer

Answer: ((c))

Y 1 O

Given series:

Left side S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £ Right side

Here, the group is formed in which second element is third to the right of the first element, and the third element is to the immediate right of the second element:

@ T # → S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £
W 4 6 → S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £
Y 1 O → S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £ (As 1 is second to the right of Y and O is second o the right of 1)
$ © 7 → S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £
9 & 4 → S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £

Y 1 O does not belong to the group.

Hence, Y 1 O is the correct answer.

How many such alphabets are there in the above arrangement each of which is not immediately followed by a symbol?

((a))
Six
((b))
Two
((c))
Five
((d))
Three
((e))
Four

Show Answer

Answer: ((c))

Five

Given series:

Left side S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £ Right side

Alphabets in the above arrangement each of which is not immediately followed by a symbol:

The required order is: Alphabet→ Number/ Alphabet

S Y % 1 8 O 9 W A & 4 6 E * 2 @ U 5 T # B $ N 3 © 7 £

Hence, there are five alphabets in the above arrangement each of which is not immediately followed by a symbol: S Y, O 9, W A, U 5, N 3

Directions: Answer the questions based on the information given below:

654 483 635 928 519

If first and third digits of each number are interchanged then what is the sum of the highest and the second lowest number thus formed?

((a))
1400
((b))
1371
((c))
1467
((d))
1208
((e))
1582

Show Answer

Answer: ((b))

1371

Given numbers:

654 483 635 928 519

Interchanging first and third digits, we get: 456 384 536 829 915

The highest number is 915 and the second lowest number is 456.

915 + 456 = 1371

Hence, 1371 is the sum of the highest and the second lowest number.

If 2 is subtracted from all the given numbers then how many numbers are there in the new arrangement which are multiples of 3?

((a))
Three
((b))
None
((c))
Two
((d))
One
((e))
Four

Show Answer

Answer: ((d))

One

Given numbers:

654 483 635 928 519

On subtracting 2 from the given numbers, we get: 652 481 633 926 517

Hence, only one number i.e., 633 is a multiple of 3 which is obtained from 635.

What is the product of the highest digit of the fourth highest number and the lowest digit of the highest number?

((a))
18
((b))
12
((c))
6
((d))
24
((e))
15

Show Answer

Answer: ((a))

Given numbers:

654 483 635 928 519

Arranging the numbers in decreasing order.

928, 654, 635, 519, 483

First highest - 928

Second highest - 654

Third highest - 635

Fourth highest - 519

Fifth highest or youngest - 483

The fourth highest number is 519 and its highest digit is 9.

The highest number is 928 and its lowest digit is 2.

The multiplication is: 9 × 2 = 18

Hence, 18 is the product of the numbers.

If the digits of each number are arranged in ascending order within the numbers, then what is the difference between the highest and the lowest number thus formed?

((a))
286
((b))
197
((c))
397
((d))
315
((e))
297

Show Answer

Answer: ((e))

297

Given numbers:

654 483 635 928 519

On arranging the digits in ascending order within the number, we get: 456 348 356 289 159

The highest number is 456 and the lowest number is 159.

456 – 159 = 297

Hence, 297 is the resultant.

Direction: Study the information given below carefully and answer the questions that follow.

Six persons A, B, C, D, E, and F have seminars in February, March, and August with two seminars in each month. The seminar is scheduled either on 9th or 20th of the month. E attends the seminar on the odd numbered date. The number of people attending the seminar before B is same as the number of people attending after C. F is not the last one to attend the seminar. There is only one person attending the seminar between A and B. A attends the seminar on odd numbered date in the month having odd number of days. C attends the seminar in March. The year is not a leap year.

Who is the last one to attend the seminar?

((a))
C
((b))
E
((c))
B
((d))
A
((e))
D

Show Answer

Answer: ((e))

Given:

People: A, B, C, D, E, and F

Months: February, March, and August

Dates: 9th or 20th of the month

A attends the seminar on odd numbered date in the month having odd number of days.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th
20th
August (31)	9th	A
20th

Case 2:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th
20th

There is only one person attending the seminar between A and B.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th	B
20th

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th

The number of people attending the seminar before B is same as the number of people attending after C.
C attends the seminar in March. (This eliminate Case 2 (a) and Case 2 (b).

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th	C
March (31)	9th	A
20th
August (31)	9th	B
20th

This case is eliminated as C is not attending in March here.

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th	C

This case is eliminated as C is not attending in March here.

5) E attends the seminar on the odd numbered date.

F is not the last one to attend the seminar.

Case 1:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Thus, the final arrangement:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th	D

Hence, D is the last one to attend the Seminar.

F attends the seminar on ______?

((a))
20th March
((b))
20th August
((c))
9th February
((d))
20th February
((e))
9th August

Show Answer

Answer: ((d))

20th February

Given:

People: A, B, C, D, E, and F

Months: February, March, and August

Dates: 9th or 20th of the month

A attends the seminar on odd numbered date in the month having odd number of days.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th
20th
August (31)	9th	A
20th

Case 2:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th
20th

There is only one person attending the seminar between A and B.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th	B
20th

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th

The number of people attending the seminar before B is same as the number of people attending after C.
C attends the seminar in March. (This eliminate Case 2 (a) and Case 2 (b).

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th	C
March (31)	9th	A
20th
August (31)	9th	B
20th

This case is eliminated as C is not attending in March here.

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th	C

This case is eliminated as C is not attending in March here.

5) E attends the seminar on the odd numbered date.

F is not the last one to attend the seminar.

Case 1:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Thus, the final arrangement:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th	D

Hence, F attends the seminar on 20th February.

Who attends the seminar between F and A?

((a))
B and C
((b))
D and A
((c))
C and E
((d))
only B
((e))
None of the above

Show Answer

Answer: ((a))

B and C

Given:

People: A, B, C, D, E, and F

Months: February, March, and August

Dates: 9th or 20th of the month

A attends the seminar on odd numbered date in the month having odd number of days.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th
20th
August (31)	9th	A
20th

Case 2:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th
20th

There is only one person attending the seminar between A and B.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th	B
20th

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th

The number of people attending the seminar before B is same as the number of people attending after C.
C attends the seminar in March. (This eliminate Case 2 (a) and Case 2 (b).

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th	C
March (31)	9th	A
20th
August (31)	9th	B
20th

This case is eliminated as C is not attending in March here.

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th	C

This case is eliminated as C is not attending in March here.

5) E attends the seminar on the odd numbered date.

F is not the last one to attend the seminar.

Case 1:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Thus, the final arrangement:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th	D

Hence, B and C attends the seminar between F and A

How many persons attends the seminar after E?

((a))
Four
((b))
Three
((c))
One
((d))
Two
((e))
Five

Show Answer

Answer: ((e))

Five

Given:

People: A, B, C, D, E, and F

Months: February, March, and August

Dates: 9th or 20th of the month

A attends the seminar on odd numbered date in the month having odd number of days.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th
20th
August (31)	9th	A
20th

Case 2:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th
20th

There is only one person attending the seminar between A and B.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th	B
20th

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th

The number of people attending the seminar before B is same as the number of people attending after C.
C attends the seminar in March. (This eliminate Case 2 (a) and Case 2 (b).

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th	C
March (31)	9th	A
20th
August (31)	9th	B
20th

This case is eliminated as C is not attending in March here.

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th	C

This case is eliminated as C is not attending in March here.

5) E attends the seminar on the odd numbered date.

F is not the last one to attend the seminar.

Case 1:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Thus, the final arrangement:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th	D

Hence, five persons attends the seminar after E.

A attends the seminar in which month?

((a))
February
((b))
March
((c))
August
((d))
Either February or March
((e))
Either March or August

Show Answer

Answer: ((c))

August

Given:

People: A, B, C, D, E, and F

Months: February, March, and August

Dates: 9th or 20th of the month

A attends the seminar on odd numbered date in the month having odd number of days.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th
20th
August (31)	9th	A
20th

Case 2:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th
20th

There is only one person attending the seminar between A and B.

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	A
20th
August (31)	9th	B
20th

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th

The number of people attending the seminar before B is same as the number of people attending after C.
C attends the seminar in March. (This eliminate Case 2 (a) and Case 2 (b).

Case 1:

Month	Dates	Person
February (28)	9th
20th
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Case 2 (a):

Month	Dates	Person
February (28)	9th
20th	C
March (31)	9th	A
20th
August (31)	9th	B
20th

This case is eliminated as C is not attending in March here.

Case 2 (b):

Month	Dates	Person
February (28)	9th	B
20th
March (31)	9th	A
20th
August (31)	9th
20th	C

This case is eliminated as C is not attending in March here.

5) E attends the seminar on the odd numbered date.

F is not the last one to attend the seminar.

Case 1:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th

Thus, the final arrangement:

Month	Dates	Person
February (28)	9th	E
20th	F
March (31)	9th	B
20th	C
August (31)	9th	A
20th	D

Hence, A attends the seminar on August.

Numerical Ability (40 questions)

The ratio of the speed of a boat in still water and the speed of the stream is 5 : 1. If the speed of travelling downstream is 24 km/hr, then find the time taken by boat to cover 48 km while moving upstream

((a))
3 hrs
((b))
2 hrs
((c))
5 hrs
((d))
6 hrs
((e))
4 hrs

Show Answer

Answer: ((a))

3 hrs

Given:

Speed of boat in still water : Speed of stream = 5 : 1

Downstream speed = 24 kmph

Formula used:

Distance/time = speed

Downstream speed = Speed of boat in still water + Speed of stream

Upstream speed = Speed of boat in still water – Speed of stream

Calculation:

Let the speed of the boat in still water and speed of the stream be 5x and x respectively

According to the question,

5x + x = 24

x = 4

Upstream speed = 5x – x = 16 kmph

∴ Required time = 48/16 = 3 hours

The height of a right angled triangle is equal to the side of the square whose diagonal is 18√2 cm. If the area of the triangle is 108 cm², what will be the base of the triangle?

((a))
12 cm
((b))
10 cm
((c))
8 cm
((d))
6 cm
((e))
9 cm

Show Answer

Answer: ((a))

12 cm

Given:

Area of triangle = 108 cm²

Diagonal of square = 18√2 cm

Formula used:

Area of triangle = ½ × base × height

Diagonal = √2 × side

Calculation:

Side of square = 18√2/√2 = 18 cm

⇒ Height of triangle = 18 cm

According to the question,

108 = ½ × base × 18

∴ Base = 108 × 2/18 = 12 cm

Direction: Read the following Bar graph carefully and answer the following questions:

The following bar graph shows the number of visitors to the Taj Mahal in the first week of January.

The number of visitors on Saturday is what percentage more than that of Friday.

((a))
25%
((b))
30%
((c))
50%
((d))
20%
((e))
40%

Show Answer

Answer: ((e))

40%

Number of visitors on Saturday = 3500

Number of visitors on Friday = 2500

∴ Required percent = (3500 – 2500)/2500 × 100 = 40%

Find the average of all the visitors who visited the Taj Mahal from Monday to Friday.

((a))
3200
((b))
3000
((c))
3300
((d))
2800
((e))
None of these

Show Answer

Answer: ((c))

3300

Number of visitors from Monday to Friday = 2000 + 4000 + 5000 + 3000 + 2500 = 16500

∴ Required average = 16500/5 = 3300

Find on which day the number of visitors to the Taj Mahal is the highest?

((a))
Monday
((b))
Tuesday
((c))
Wednesday
((d))
Thursday
((e))
Friday

Show Answer

Answer: ((c))

Wednesday

Number of visitors on Monday = 2000

Number of visitors on Tuesday = 4000

Number of visitors on Wednesday = 5000

Number of visitors on Thursday = 3000

Number of visitors on Friday = 2500

Number of visitors on Saturday = 3500

∴ Maximum number of visitors is on Wednesday.

The ratio of male and female visitors on Friday is 3 ∶ 2. Find the difference between the number of male and female visitors.

((a))
600
((b))
500
((c))
450
((d))
300
((e))
None of these

Show Answer

Answer: ((b))

500

Number of male visitors on Friday = 3/5 × 2500 = 1500

Number of female visitors on Friday = 2/5 × 2500 = 1000

∴ Required difference = 1500 – 1000 = 500

Find the ratio of visitors who visited the Taj Mahal on Monday and Thursday.

((a))
2 ∶ 3
((b))
3 ∶ 2
((c))
3 : 1
((d))
1 : 3
((e))
None of these

Show Answer

Answer: ((a))

2 ∶ 3

Number of visitors on Monday = 2000

Number of visitors on Thursday = 3000

∴ Required ratio = 2000 : 3000 = 2 : 3

A man invested some amount P at the rate of 20% for 2 years compounded annually and earned 792 as interest. Find the value of P.

((a))
Rs. 1200
((b))
Rs. 1450
((c))
Rs. 1600
((d))
Rs. 1800
((e))
Rs. 2000

Show Answer

Answer: ((d))

Rs. 1800

Given:

R = 20%, T = 2 years

CI = Rs. 792

Formula used:

CI = P(1 + R/100)^T – P

Calculation:

792 = P(1 + 20/100)² – P

⇒ 792 = 0.44P

∴ P = Rs. 1800

Given:

R = 20%, T = 2 years

Formula used:

Effective rate of interest = 20 + 20 +(20 × 20)/100 = 44%

100% = Amount

⇒ 792 = 44%

⇒ 72 = 4%

⇒ 18 = 1%

⇒ 100% = Rs. 1800

3 years ago, ratio of ages between A and B is 3: 4 and 3 year hence ratio of ages between A and B is 4: 5. Find the ratio between their present ages:

((a))
9: 7
((b))
5: 7
((c))
7: 5
((d))
7: 9
((e))
None of these

Show Answer

Answer: ((d))

7: 9

Given:

3 years ago, A : B = 3 : 4

3 years hence, A : B = 4 : 5

Concept:

Here we will be using the basic concept of ratio.

Calculation:

Let the ages of A and B 3 years ago be 3x and 4x respectively

So present age of A will be 3x + 3 and

3 year hence the age of A = 3x + 3 + 3

Same is for age of B

Now,

⇒ (3x + 3 + 3) / (4x + 3 + 3) = 4/5

⇒ 5 × (3x + 6) = 4 × (4x + 6)

⇒ 15x + 30 = 16x + 24

⇒ x = 6

Present age of A = 3x + 3 = 21 years

Present age of B = 4x + 3 = 27 years

∴ Required ratio = 21 : 27 = 7 : 9

Direction: Read the following table carefully and answer the questions given below:

The given table shows the number of boys and girls in 5 different school:

Schools	Number of boys	Number of girls
A	80	50
B	90	60
C	70	40
D	70	90
E	90	80

Find the total number of girls in school C and E together is how much percent more or less than the total number of students in school D.

((a))
25% more
((b))
30% more
((c))
30% less
((d))
25% less
((e))
20% more

Show Answer

Answer: ((d))

25% less

The total number of girls in school C = 40

The total number of girls in school E = 80

The total number of girls in school C and E = 40 + 80 = 120

The total number of girls in school D = 90

The total number of boys in school D = 70

The total number of students in school D = 90 + 70 = 160

Now to find the total number of girls in school C and E together is less percent than to the total number of students in school D

⇒ [(160 – 120)/160] × 100 = 25% less

∴ the total number of girls in school C and E together is 25% less than the total number of students in school B

Find the ratio between the average number of girls in school B and D together and the average number of boys in school B and C together.

((a))
16 ∶ 15
((b))
8 : 5
((c))
15 : 16
((d))
5 : 8
((e))
None of these

Show Answer

Answer: ((c))

15 : 16

The total number of girls in school B = 60

The total number of girls in school D = 90

Now to find the average number of girls in school B and D

⇒ (The total number of girls in school B + The total number of girls in school D)/2

⇒ (60 + 90)/2 = 75

The total number of boys in school B = 90

The total number of boys in school C = 70

Now to find the average number of boys in school B and C

⇒ (The total number of girls in school B + The total number of girls in school C)/2

⇒ (90 + 70)/2 = 80

Now to find the ratio between the average number of girls in school B and D together and the average number of boys in school B and C together

⇒ 75 ∶ 80 = 15 ∶ 16

∴ The ratio between the average number of girls in school B and D together and the average number of boys in school B and C together is 15 ∶ 16.

The total number of girls in school E is what percent of the total number of students in school D?

((a))
200%
((b))
50%
((c))
70%
((d))
25%
((e))
None of these

Show Answer

Answer: ((b))

50%

The total number of girls in school E = 80

The total number of girls in school D = 90

The total number of boys in school D = 70

The total number of students in school D = 90 + 70 = 160

Now to find the total number of girls in school E is what percent of the total number of students in school D

⇒ (The total number of girls in school E/the total number of students in school D) × 100

⇒ (80/160) × 100 = 50%

Find the ratio between the total number of students in school D and the total number of student in school A.

((a))
13 ∶ 16
((b))
7 ∶ 6
((c))
6 : 7
((d))
16 ∶ 13
((e))
None of these

Show Answer

Answer: ((d))

16 ∶ 13

The total number of girls in school D = 90

The total number of boys in school D = 70

The total number of students in school D = 90 + 70 = 160

The total number of girls in school A = 50

The total number of boys in school A = 80

The total number of students in school A = 50 + 80 = 130

Now to find the ratio between the total number of students in school D and the total number of students in school A

⇒ The total number of students in school D ∶ The total number of students in school A

⇒ 160 ∶ 130 = 16 ∶ 13

∴ The ratio between the total number of students in school D and the total number of students in school A is 16 ∶ 13.

Find the average number of girls in schools B, C, and E.

((a))
66
((b))
40
((c))
70
((d))
60
((e))
80

Show Answer

Answer: ((d))

Formula used:

Average = total number of girls/The total number of school

Calculation:

The total number of girls in school B = 60

The total number of girls in school C = 40

The total number of girls in school E = 80

The total number of girls in schools B, C, and E = 60 + 40 + 80 = 180

Now to find the average number of girls in schools B, C, and E = 180/3 = 60

∴ The average number of girls in schools B, C, and E is 60.

What should come in place of the question mark '?' in the following number series?

16, 24, 36, ?, 72

((a))
48
((b))
52
((c))
56
((d))
42
((e))
60

Show Answer

Answer: ((b))

16 + 8 = 24

24 + 12 = 36

36 + 16 = 52

52 + 20 = 72

∴ 52 will come in place of question mark.

What should come in place of the question mark '?' in the following number series?

2, 6, 22, ?, 65814

((a))
96
((b))
58
((c))
278
((d))
198
((e))
76

Show Answer

Answer: ((c))

278

2 + 2² = 6

6 + 2⁴ = 22

22 + 2⁸ = 278

278 + 2¹⁶ = 65814

∴ 278 will come in place of question mark.

What should come in place of the question mark '?' in the following number series?

288, 275, 262, 249, ?

((a))
249
((b))
223
((c))
210
((d))
262
((e))
236

Show Answer

Answer: ((e))

236

288 – 13 = 275

275 – 13 = 262

262 – 13 = 249

249 – 13 = 236

∴ 236 will come in place of question mark.

What should come in place of the question mark '?' in the following number series?

289, 324, 361, ?, 441

((a))
384
((b))
400
((c))
396
((d))
411
((e))
376

Show Answer

Answer: ((b))

400

17² = 289

18² = 324

19² = 361

20² = 400

21² = 441

∴ 400 will come in place of question mark.

What should come in place of the question mark '?' in the following number series?

12, 20, 47, 111, ?, 452

((a))
236
((b))
412
((c))
263
((d))
336
((e))
381

Show Answer

Answer: ((a))

236

12 + 2³ = 20

20 + 3³ = 47

47 + 4³ = 111

111 +5³ = 236

236 + 6³ = 452

∴ 236 will come in place of question mark.

Directions: Read the given information carefully and answer the following questions.

A and B invested in a business in the ratio 4 : 5. A invested for 4 months more than B. At the end of year, the total profit earned is Rs. 35000 out of which B earned Rs. 15000.

What is the ratio of the time period of investment of A and B?

((a))
3 : 2
((b))
5 : 3
((c))
2 : 1
((d))
4 : 1
((e))
5 : 2

Show Answer

Answer: ((b))

5 : 3

Given:

Investment ratio of A and B = 4:5.

Time invested by A = 4 months more than B.

Total profit = Rs. 35000.

Profit earned by B = Rs. 15000.

Formula Used:

Profit share ratio = (Investment × Time) ratio.

Calculation:

Let investment of A = 4x, and B = 5x.

Let time invested by B = t months, then A invested for t + 4 months.

Profit ratio = Profit of A : Profit of B.

From total profit, Profit of A = Rs. 35000 - Rs. 15000 = Rs. 20000.

Profit ratio = 20000 : 15000 = 4 : 3.

Setting up equation from profit ratio:

⇒ (4x × (t + 4)) / (5x × t) = 4 / 3

Removing x as it cancels out:

⇒ (4 × (t + 4)) / (5 × t) = 4 / 3

Cross multiply to solve for t:

⇒ 12 × (t + 4) = 20 × t

⇒ 12t + 48 = 20t

⇒ 8t = 48

⇒ t = 6

Time invested by B = 6 months, and A = 6 + 4 = 10 months.

Time ratio of A to B = 10 months : 6 months = 5 : 3.

The ratio of the time period of investment of A and B is 5:3.

What is the amount invested by A in the business?

((a))
Rs. 16000
((b))
Rs. 20000
((c))
Rs. 18000
((d))
Rs. 22000
((e))
Cannot be determined

Show Answer

Answer: ((e))

Cannot be determined

Let the amount invested by A and B be 4x and 5x respectively

Let B invested by ‘t’ months

Time of investment of A = t + 4

Profit ratio = 4x × (t + 4) : 5x × t = (4t + 16) : 5t

Now, B’s share:

5t/(4t + 16 + 5t) × 35000 = 15000

35t = 27t + 48

8t = 48

t = 6 months

Period of investment: A = 10 months, B = 6 months

Amount invested by A = 4x

We cannot determine the value of ‘x’

∴ Amount invested by A cannot be determined.

Here many might mistake 'by the end of year' as one year and solve the question and get it wrong. Note that it is not written 'by the end of one year', since no numerical value of time is given, and with only the ratio given we can not reach a valid conclusion.

Another person C invested Rs 1,80,000 at simple interest at the rate of 10% per annum for the same time period as A invested. Find the interest earned by him?

((a))
Rs. 15,000
((b))
Rs. 24,000
((c))
Rs. 30,000
((d))
Rs. 40,000
((e))
None of these

Show Answer

Answer: ((a))

Rs. 15,000

Let the amount invested by A and B be 4x and 5x respectively

Let B invested by ‘t’ months

Time of investment of A = t + 4

Profit ratio = 4x × (t + 4) : 5x × t = (4t + 16) : 5t

Now, B’s share:

5t/(4t + 16 + 5t) × 35000 = 15000

35t = 27t + 48

8t = 48

t = 6 months

Period of investment: A = 10 months, B = 6 months

∴ Required time of investment of A = 10 months

Investment of C = 1,80,000

Time period is same as for A

Rate of interest = 10%

SI = PRT/100

= (1,80,000 x 10 x 10/12)/100

= 15,000

A mixture contains 100 litres of milk and 40 litres of water. If the milkman added 40 litres of water in the mixture then find the ratio of milk and water in the new mixture.

((a))
5 : 4
((b))
4 : 5
((c))
3 : 4
((d))
4 : 7
((e))
7 : 4

Show Answer

Answer: ((a))

5 : 4

Given:

Milk = 100 L and water = 40 L

Calculation:

Quantity of water after addition = 40 + 40 = 80 L

∴ Required ratio = 100 : 80 = 5 : 4

A tank has two inlet pipe which can fill the tank in 3 hours and 4 hours respectively and has one outlet pipe which can empty the tank in 6 hours. If all the pipes work together then in how many hours the tank will be filled?

((a))
5/12 hours
((b))
11/12 hours
((c))
12/5 hours
((d))
5/9 hours
((e))
7/12 hours

Show Answer

Answer: ((c))

12/5 hours

Given:

Time: Inlet pipe = 3 hours and 4 hours, Outlet pipe = 6 hours

Formula used:

If inlet pipes take a and b hours to fill while the outlet pipe takes c hours to empty then time taken when all 3 pipes work,

1/t = 1/a + 1/b – 1/c

Calculation:

Let the required time be ‘t’

1/t = 1/3 + ¼ - 1/6 = (4 + 3 – 2)/12

t = 12/5 hours

∴ Required time = 12/5 hours

What will come in place of question mark (?) in the following equation?

2500 + (450/?) ÷ 9 = 2550

((a))
2
((b))
4
((c))
6
((d))
1
((e))
-2

Show Answer

Answer: ((d))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

2500 + (450/?) ÷ 9 = 2550

2500 + 50/? = 2550

⇒ 50/? = 50

⇒ ? = 1

What will come in place of question mark (?) in the following equation?

25% of 60 + 20% of 45 = ?

((a))
24
((b))
27
((c))
30
((d))
32
((e))
36

Show Answer

Answer: ((a))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

25/100 × 60 + 20/100 × 45 = ?

⇒ 15 + 9 = ?

⇒ ? = 24

What will come in place of question mark (?) in the following equation?

$?+ \frac{1}{3} + 2\frac{2}{3} + 4\frac{1}{4} = 8\frac{1}{4}$

((a))
-1
((b))
-2
((c))
2
((d))
1
((e))
3

Show Answer

Answer: ((d))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

? + 1/3 + 2 + 2/3 + 4 + ¼ = 8 + ¼

⇒ ? = 8 – (4 + 2) – (2/3 + 1/3)

⇒ ? = 2 – 1 = 1

What will come in place of question mark (?) in the following equation?

1156 + 984 - 2256 + 166 = ?

((a))
40
((b))
50
((c))
60
((d))
70
((e))
80

Show Answer

Answer: ((b))

Concept used:

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

Calculation:

1156 + 984 - 2256 + 166 = ?

2306 – 2256 = ?

⇒ ? = 50

∴ The value of ? is 50

What will come in place of question mark (?) in the following equation?

√(12 × 4 - 12 + 28) = ?

((a))
6
((b))
4
((c))
2
((d))
12
((e))
8

Show Answer

Answer: ((e))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

√(48 – 12 + 28) = ?

⇒ √64 = ?

⇒ ? = 8

What will come in place of question mark (?) in the following equation?

?² = (7 + 11) × (19 + 13)

((a))
28
((b))
22
((c))
24
((d))
26
((e))
18

Show Answer

Answer: ((c))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

?² = 18 × 32

⇒ ?² = 576

⇒ ? = 24

What will come in place of question mark (?) in the following equation?

(√25 × 12) ÷ 15 + √256 = ?

((a))
15
((b))
12
((c))
18
((d))
25
((e))
20

Show Answer

Answer: ((e))

Concept used:

Follow the BODMAS rule according to the table given below:

Calculations:

(√25 × 12) ÷ 15 + √256 = ?

⇒ (5 × 12)/15 + 16 = ?

⇒ 4 + 16 = ?

⇒ ? = 20

What will come in place of question mark (?) in the following equation?

(15/11) × 143 + 30 = ?²

((a))
12
((b))
25
((c))
10
((d))
8
((e))
15

Show Answer

Answer: ((e))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

15 × 13 + 30 = ?²

⇒ ?² = 225

⇒ ? = 15

What will come in place of question mark (?) in the following equation?

12.5% of 80 - ? = 10% of 60

((a))
6
((b))
8
((c))
2
((d))
12
((e))
4

Show Answer

Answer: ((e))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

12.5/100 × 80 - ? = 10/100 × 60

⇒ 10 - ? = 6

⇒ ? = 4

What will come in place of question mark (?) in the following equation?

15 × ? + 26 × 4 = 284

((a))
8
((b))
16
((c))
12
((d))
10
((e))
14

Show Answer

Answer: ((c))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

15 × ? + 104 = 284

⇒ 15 × ? = 180

⇒ ? = 12

What will come in place of question mark (?) in the following equation?

115 ÷ 5 + 12 × 1.5 = ?

((a))
51
((b))
41
((c))
43
((d))
47
((e))
49

Show Answer

Answer: ((b))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

23 + 18 = ?

⇒ ? = 41

What will come in place of question mark (?) in the following equation?

33 + 12 × 4 = ? + 5²

((a))
40
((b))
55
((c))
45
((d))
30
((e))
50

Show Answer

Answer: ((e))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

27 + 48 = ? + 25

⇒ ? = 75 – 25

⇒ ? = 50

What will come in place of question mark (?) in the following equation?

(18 × 6) - (5² × 4) = √?

((a))
4
((b))
16
((c))
8
((d))
64
((e))
36

Show Answer

Answer: ((d))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

108 – 25 × 4 = √?

⇒ ? = 8²

⇒ ? = 64

What will come in place of question mark (?) in the following equation?

(24/5) ÷ (12/35) + 12² = ? + 18

((a))
140
((b))
160
((c))
120
((d))
150
((e))
180

Show Answer

Answer: ((a))

140

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

24/5 × 35/12 + 144 = ? + 18

⇒ 14 + 144 – 18 = ?

⇒ ? = 158 – 18

⇒ ? = 140

What will come in place of question mark (?) in the following equation?

126 + 228 + 26 × 5 = ?²

((a))
22
((b))
32
((c))
14
((d))
18
((e))
16

Show Answer

Answer: ((a))

Concept used:

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 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 least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

Calculations:

354 + 130 = ?²

⇒ ?² = 484

⇒ ? = 22

If 24 men can complete a work in 40 days, then 1/3rd of total men will complete the same work in:

((a))
80 days
((b))
90 days
((c))
120 days
((d))
150 days
((e))
180 days

Show Answer

Answer: ((c))

120 days

Given:

24 men can complete a work in 40 days

Formula used:

M₁D₁ = M₂D₂ (M = number of men, D = number of days)

Calculation:

New number of men = 1/3 × 24 = 8

∴ Required number of days = (24 × 40)/8

= 120 days

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