RRB Clerk Prelims Memory Based Paper (Held On: 18 August 2024 Shift 2) (Previous Year Paper)

Number of person living above Oliver's floor is the same as number of person living below Oliver's floor. It means Oliver lives in  floor number 4 There are only two floor below Lian's floor.

Floor in which Lian lives is four floors below from James who lives immediately above Aaron floor. It means There will be three floor in between Lian and James.

There are four people living in between Aaron and Finn floor.  Henry does not live below Lian.

Final arrangement 

After arranging in alphabetical order 

Henry, Lian, and Noah will be in the same place even after the rearrangement. 

Hence three is the correct answer

Number of person living above Oliver's floor is the same as number of person living below Oliver's floor. It means Oliver lives in  floor number 4 There are only two floor below Lian's floor.

Floor in which Lian lives is four floors below from James who lives immediately above Aaron floor. It means There will be three floor in between Lian and James.

There are four people living in between Aaron and Finn floor.  Henry does not live below Lian.

Final arrangement 

Hence henry lives in floor number five.

Number of person living above Oliver's floor is the same as number of person living below Oliver's floor. It means Oliver lives in  floor number 4 There are only two floor below Lian's floor.

Floor in which Lian lives is four floors below from James who lives immediately above Aaron floor. It means There will be three floor in between Lian and James.

There are four people living in between Aaron and Finn floor.  Henry does not live below Lian.

Final arrangement 

There are two floor in between Oliver and Finn's floor.

Number of person living above Oliver's floor is the same as number of person living below Oliver's floor. It means Oliver lives in  floor number 4 There are only two floor below Lian's floor.

Floor in which Lian lives is four floors below from James who lives immediately above Aaron floor. It means There will be three floor in between Lian and James.

There are four people living in between Aaron and Finn floor.  Henry does not live below Lian.

Final arrangement 

Hence Noah lives two floor below Oliver floor is correct statement.

Number of person living above Oliver's floor is the same as number of person living below Oliver's floor. It means Oliver lives in  floor number 4 There are only two floor below Lian's floor.

Floor in which Lian lives is four floors below from James who lives immediately above Aaron floor. It means There will be three floor in between Lian and James.

There are four people living in between Aaron and Finn floor.  Henry does not live below Lian.

Final arrangement 

Noah is related to Aaron and Finn is related to Henry  there are three floor in between them hence Lian is related to James.

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

I. Few disk are not flip →True (Because given only a few means that only some disk are flip remaining are not flip)

II. Some flip are computers → False (Because there is no relation between flip and computers)

Hence, Only I is true.

Important Points

Only a few is the case of some + some not and only few is consider as some.

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

Conclusions:

I. Some pipes being powder is a possibility →True (As we can see that no direct relationship between the two is given, so the part of pipe which is not Brick can be the part of reamining powder which is not cement).

II. Some powder being bricks is a possibility → True (The remaining portion of powder which is not cement, can be the part of bricks, the possibility is true).

Hence, Both I and II follow

Possible Venn Diagram for given Statements:- 

Conclusions:

Some flowers are stem. → False (as only leaves are flowers.)

No petal is flowers. → True (as only leaves are flowers.)

Hence, Only conclusion II is true.

The Least possible venn diagram is

conclusion I → True ( As we can see that some gentlemen are women, So this statement is true)

conclusion II → False (From below figure we can see that some women can be men and still all given statements stand true, hence no women is men is possible but not definite)

Hence Only conclusion I follow.

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

 I. Some cricketers are not players → False (It is a possibility but not definite as we have not given anything about cricketers with respect to the players)

 II. Some cricketers are rich → False (It is a possibility but not definite)

Hence, Neither I nor II follows.

Given words: PED      DFR      FIK      TIS     SND

1. Changing all letters to previous alphabet as per English alphabetical series:

ODC   CEQ   EHJ   SHR   RMC

2. Clearly, 3 words ODC   CEQ   EHJ have vowels.

Note: In English alphabetical series there are 5 vowels i.e., A, E, I, O, U and remaining alphabets all are called consonants.

Hence, three words having vowels will be formed.

Given words: PED      DFR      FIK      TIS      SND

1. Arranging words in the order as they appear in a dictionary from right to left:

Left side    TIS    SND   PED    FIK   DFR   Right side

Hence, TIS  is the fifth from right.

Given words: PED      DFR      FIK      TIS      SND

Clearly two meaningful word  ITS and SIT can be formed.

Hence, two word can be formed.

Given words: PED      DFR      FIK      TIS      SND

1. First and last letter is replaced by immediate succeeding letter as per alphabetical series:

QEE      EFS      GIL      UIT      TNE

2. Clearly, two words QEE and UIT has more than one vowel.

Note: In English alphabetical series there are 5 vowels i.e. A, E, I, O, U remaining alphabets are consonants.

Hence, two words have more than one vowel after rearrangement.

Given words: PED      DFR      FIK      TIS      SND

Left side   PED      DFR      FIK      TIS      SND  Right side

1. Second letter of the word which is fourth from the left side: PED      DFR      FIK      TIS     

2. First letter of the word which is first from the right side: SND

3. Clearly, there are 9 letters between I and S:

I  J  K  L  M  N  O P Q R S

Hence, 9 letters are between I and S.

Odd numbers → Next digit

Even numbers → Previous digit

Replaced number: 2 7 4 6 1 8 5

Second digit from left end: 7

Third digit from right end: 1

Sum of both the numbers: 7 + 1 = 8

Hence, ‘8’ is the right answer.

Family tree,

1.R is male member of the family

2. L is the only son of C, who is the brother of R 3. T is the wife of L 4. Q is the daughter in law of P, who is grand mother of L. 

Two cases will be 

5.T is not a daughter in law of Q. hence final arrangement will be

Hence C is brother in law of Q.

Family tree,

1.R is male member of the family

2. L is the only son of C, who is the brother of R 3. T is the wife of L 4. Q is the daughter in law of P, who is grand mother of L. 

Two cases will be 

5.T is not a daughter in law of Q. hence final arrangement will be

L is the Nephew of R.

Family tree,

1.R is male member of the family

2. L is the only son of C, who is the brother of R 3. T is the wife of L 4. Q is the daughter in law of P, who is grand mother of L. 

Two cases will be 

5.T is not a daughter in law of Q. hence final arrangement will be

Hence, T is the wife of L, who is Nephew of Q.

From the given information,

Row 1: A, B, C, D and E are facing South

Row 2: P, Q, R, S and T are facing North

1. T sits third to the left of S.

Following are the possibilities we get:

Case 1:

Case 2:

2. B faces immediate neighbor of T.

3. A sit second to the right of B.

The above conditions are not satisfied in case 2. So, it will be eliminated.

Case 1:

4. Only one person sits between C and E.

Case 1 (a):

Case 1 (b):

5. R and Q are immediate neighbours.

6. Q faces neither B nor C.

7. P doesn’t face D.

The above conditions are not satisfied in case 1 (b). So, it will be eliminated.

The final arrangement will be as shown below:

Hence, two persons are sitting between C and D.

From the given information,

Row 1: A, B, C, D and E are facing South

Row 2: P, Q, R, S and T are facing North

1. T sits third to the left of S.

Following are the possibilities we get:

Case 1:

Case 2:

2. B faces immediate neighbor of T.

3. A sit second to the right of B.

The above conditions are not satisfied in case 2. So, it will be eliminated.

Case 1:

4. Only one person sits between C and E.

Case 1 (a):

Case 1 (b):

5. R and Q are immediate neighbors.

6. Q faces neither B nor C.

7. P doesn’t face D.

The above conditions are not satisfied in case 1 (b). So, it will be eliminated.

The final arrangement will be as shown below:

Hence, Q faces E.

From the given information,

Row 1: A, B, C, D and E are facing South

Row 2: P, Q, R, S and T are facing North

1. T sits third to the left of S.

Following are the possibilities we get:

Case 1:

Case 2:

2. B faces immediate neighbor of T.

3. A sit second to the right of B.

The above conditions are not satisfied in case 2. So, it will be eliminated.

Case 1:

4. Only one person sits between C and E.

Case 1 (a):

Case 1 (b):

5. R and Q are immediate neighbors.

6. Q faces neither B nor C.

7. P doesn’t face D.

The above conditions are not satisfied in case 1 (b). So, it will be eliminated.

The final arrangement will be as shown below:

Hence, none of these is correct.

From the given information,

Row 1: A, B, C, D and E are facing South

Row 2: P, Q, R, S and T are facing North

1. T sits third to the left of S.

Following are the possibilities we get:

Case 1:

Case 2:

2. B faces immediate neighbor of T.

3. A sit second to the right of B.

The above conditions are not satisfied in case 2. So, it will be eliminated.

Case 1:

4. Only one person sits between C and E.

Case 1 (a):

Case 1 (b):

5. R and Q are immediate neighbors.

6. Q faces neither B nor C.

7. P doesn’t face D.

The above conditions are not satisfied in case 1 (b). So, it will be eliminated.

The final arrangement will be as shown below:

Hence, B and R are sitting exactly in the middle of the rows.

From the given information,

Row 1: A, B, C, D and E are facing South

Row 2: P, Q, R, S and T are facing North

1. T sits third to the left of S.

Following are the possibilities we get:

Case 1:

Case 2:

2. B faces immediate neighbor of T.

3. A sit second to the right of B.

The above conditions are not satisfied in case 2. So, it will be eliminated.

Case 1:

4. Only one person sits between C and E.

Case 1 (a):

Case 1 (b):

5. R and Q are immediate neighbors.

6. Q faces neither B nor C.

7. P doesn’t face D.

The above conditions are not satisfied in case 1 (b). So, it will be eliminated.

The final arrangement will be as shown below:

All persons except Q, are sitting at the extreme ends of the lines.

Hence, Q doesn’t belong to the group.

One pair is there in the word 'OBLIGATE', each of which has as many letters between them in the word (both forward and backward direction) as they have between them in the English Alphabet.

Mistake Points In this type of question we have to count from A to Z, reverse counting Z to A is not considered. Therefore Y- A is not the correct pair

Clearly, ‘ti’ is the code for the word ‘listen’.

Clearly, the code ‘du’ means ‘daily’.

Clearly, the code for the word ‘made’ is either ‘qa’ or ‘hu’.

The code for the word ‘hours’ is either ‘le’ or ‘pa’. The code for the word ‘happy’ must be different from the codes given in the example.

Hence, ‘pa ri’ could possibly be the code for ‘happy hours’.

Clearly, ‘mi’ is the code for the word ‘songs’.

Given statements: X ≥ Y = Z; D > N < Y

On combining: X ≥ Y = Z > N < D

Conclusions:

I. N < X → True (N < Y ≤ X; hence the relation N < X is correct)

II. Z > D → False (Z = Y > N < D; hence the relation between Z and D cannot be determined)

Therefore, only conclusion I is true.

Given statements: M > Z ≥ P ≤ U; P = B > K

On combining: M > Z ≥ P = B > K; P ≤ U

Conclusions:

I. M > U → False (M > Z ≥ P ≤ U; hence the relation between M and U cannot be determined)

II. K < U → True (K < B = P ≤ U; hence the relation K < U is correct)

Therefore, only conclusion II is true

Given statements: E > R < T, V > Z ≥ K = T

Combined Statement: V > Z ≥ K = T > R < E

Conclusions:

I. V < E → False ( as V > Z ≥ K = T > R < E → thus clear relation between V and E cannot be determined)

II. R < Z → True ( as Z ≥ K = T > R → R < T = K ≤ Z → R < Z)

Hence, only II is true.

Given statements: M ≤ B < L ≥ P; S > T ≥ P

Combined Statement: M ≤ B < L ≥ P ≤ T < S

Conclusions:

L > M → True √as M ≤ B < L → L > B ≥ M → L > M)

S ≥ P → False √as P ≤ T < S → S > T ≥ P → S > P not satisfy the condition)

Hence, Only I is True.

Given statements: O ≥ M ≤ N; N > P

On combining: O ≥ M ≤ N > P

I. O > P → False (as O ≥ M; M has no direct relation with P, so O has no relation)

II. P < N → True (on combining we conclude this)

Thus, only II follows.

People = L M, N, O, P, Q, and R

1. R spent either the least amount or the highest amount.

2. Only one person spent less than L but more than R.

It means There is one person in between L and R which is less than L and more than R.

(The second statement clearly indicates that R did not spend the highest amount. This means R spent the least amount and L is at the 5^th position.)

3. At least four people spent more than O.

(As the statement clearly indicates that O is among the bottom three. There is only one position where we can place O i.e. the 6^th position.)

4. Two people spent more than Q but less than M.

(Implies, M spent the highest amount and Q is at the 4^th position.)

5. N spent more amount than P.

(Implies, N is at the 2^nd position and P is at the 3^rd position as these are the only two position that is left to be filled in the table.)

Clearly, N spent the second-highest amount in the store.

People = L M, N, O, P, Q, and R

1. R spent either the least amount or the highest amount.

2. Only one person spent less than L but more than R.

(The second statement clearly indicates that R did not spend the highest amount. This means R spent the least amount and L is at the 5^th position.)

3. At least four people spent more than O.

(As the statement clearly indicates that O is among the bottom three. There is only one position where we can place O i.e. the 6^th position.)

4. Two people spent more than Q but less than M.

(Implies, M spent the highest amount and Q is at the 4^th position.)

5. N spent more amount than P.

(Implies, N is at the 2^nd position and P is at the 3^rd position as these are the only two position that is left to be filled in the table.)

As Q spent less than P but more than O, then the only possible amount that lies in the bracket of the spending of O and P is Rs. 600.

People = L M, N, O, P, Q, and R

1. R spent either the least amount or the highest amount.

2. Only one person spent less than L but more than R.

(The second statement clearly indicates that R did not spend the highest amount. This means R spent the least amount and L is at the 5^th position.)

3. At least four people spent more than O.

(As the statement clearly indicates that O is among the bottom three. There is only one position where we can place O i.e. the 6^th position.)

4. Two people spent more than Q but less than M.

(Implies, M spent the highest amount and Q is at the 4^th position.)

5. N spent more amount than P.

(Implies, N is at the 2^nd position and P is at the 3^rd position as these are the only two position that is left to be filled in the table.)

Clearly, M spent the highest amount.

People = L M, N, O, P, Q, and R

1. R spent either the least amount or the highest amount.

2. Only one person spent less than L but more than R.

(The second statement clearly indicates that R did not spend the highest amount. This means R spent the least amount and L is at the 5^th position.)

3. At least four people spent more than O.

(As the statement clearly indicates that O is among the bottom three. There is only one position where we can place O i.e. the 6^th position.)

4. Two people spent more than Q but less than M.

(Implies, M spent the highest amount and Q is at the 4^th position.)

5. N spent more amount than P.

(Implies, N is at the 2^nd position and P is at the 3^rd position as these are the only two position that is left to be filled in the table.)

Clearly, R spent the lowest amount.

People = L M, N, O, P, Q, and R

1. R spent either the least amount or the highest amount.

2. Only one person spent less than L but more than R.

(The second statement clearly indicates that R did not spend the highest amount. This means R spent the least amount and L is at the 5^th position.)

3. At least four people spent more than O.

(As the statement clearly indicates that O is among the bottom three. There is only one position where we can place O i.e. the 6^th position.)

4. Two people spent more than Q but less than M.

(Implies, M spent the highest amount and Q is at the 4^th position.)

5. N spent more amount than P.

(Implies, N is at the 2^nd position and P is at the 3^rd position as these are the only two position that is left to be filled in the table.)

Clearly, Q spends immediately above L.

Calculation

Number of tourists in August in B = 3600

Number of tourists in August in D = 3000

Ratio = 3600 : 3000 = 6 : 5

Calculation

July tourists in E = 4500

Let Number of tourists in July in F is x.

Then,

 4500 : x = 5 : 6

⇒ 5x = 27000

⇒ x = 5400

So, July tourists in F = 5400

August = 5400 + 450 = 5850

Calculations:

Tourists in July in C and D together = 2400 + 2000 = 4400

Tourists in August in C and D together = 3200 + 3000 = 6200

Difference = 6200 - 4400 = 1800

∴ The difference between the total number of tourists in July in C and D together and the total number of tourists in August in C and D together is 1800.

Calculations:

Number of tourists in August in B = 3600

Tourists in September = Tourists in August + 25% of Tourists in August

Tourists in September = 3600 + (25/100) × 3600

⇒ Tourists in September = 3600 + 900

⇒ Tourists in September = 4500

∴ The number of tourists in September in B is 4500.

Calculation

Total tourists in A = 3200 (July) + 2400 (August) = 5600

Ratio (M : F) = 3 : 2

Let males = (3/5) × 5600 = 3360

Females = (2/5) × 5600 = 2240

Difference (x) = 3360 − 2240 = 1120

Then, 7x = 7 × 1120 = 7840

Given:

Perimeter of the rectangle = 120 cm

Ratio of length to breadth = 7 : 8

Area of the square is 4 cm² more than the area of the rectangle.

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth

Area of square = Side²

Calculations:

Let the length = 7x and the breadth = 8x (from the ratio 7:8).

Perimeter = 2 × (Length + Breadth) = 2 × (7x + 8x) = 120

⇒ 2 × 15x = 120

⇒ 30x = 120

⇒ x = 4

Length = 7x = 7 × 4 = 28 cm

Breadth = 8x = 8 × 4 = 32 cm

Area of rectangle = Length × Breadth = 28 × 32 = 896 cm²

Let the side of the square be 's'.

Area of square = s²

We are given that the area of the square is 4 cm² more than the area of the rectangle:

s² = 896 + 4

s² = 900

⇒ s = √900

⇒ s = 30 cm

∴ The side of the square is 30 cm.

Given:

Downstream distance = 64 km

Time taken for downstream = 4 hours

Upstream distance = 48 km

Time taken for upstream = 6 hours

Formula used:

Speed = Distance ÷ Time

Speed downstream = (Speed of boat + Speed of current)

Speed upstream = (Speed of boat - Speed of current)

Calculations:

Speed downstream = 64 ÷ 4 = 16 km/hr

Speed upstream = 48 ÷ 6 = 8 km/hr

Let the speed of the boat in still water be 'b' km/hr and the speed of the current be 'c' km/hr.

Speed downstream = b + c = 16

Speed upstream = b - c = 8

Now, solving the equations:

b + c = 16

b - c = 8

Add the two equations:

(b + c) + (b - c) = 16 + 8

2b = 24

b = 12 km/hr

The speed of the boat in still water is 12 km/hr.

Now, the distance covered by the boat in 5 hours in still water is:

Distance = Speed × Time

Distance = 12 × 5 = 60 km

∴ The distance covered by the boat in 5 hours in still water is 60 km.

Given:

Investment by A = Rs. x

Investment by B = Rs. (x + 5000)

Profit share ratio of A to B = 7 : 9

Formula used:

Profit share ratio = Investment ratio (since profit is directly proportional to investment)

Calculations:

Let the total profit be P.

The ratio of profit shares of A and B is given as 7:9. So, the profit for A is 7 parts and for B is 9 parts.

The total parts = 7 + 9 = 16 parts.

The profit share of A and B is directly proportional to their investments.

Investment of A / Investment of B = Profit share of A / Profit share of B

So, x / (x + 5000) = 7 / 9

Cross multiplying:

9x = 7(x + 5000)

9x = 7x + 35000

9x - 7x = 35000

2x = 35000

x = 35000 / 2 = 17500

Now, find the value of 7x:

7x = 7 × 17500 = 122500

∴ The value of 7x is Rs. 122500.

Concept used:

Calculations:

∛1331 ÷ 11 + 95 × 100 = ?

⇒ 11 ÷ 11 + 9500 = ?

⇒ 1 + 9500 = ?

⇒ 9501 = ?

∴ The value of ? is 9501.

Concept:

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

Calulations:

Given expression is

53 ÷ 57 × 252 of 12 − 125% of 8 = ?

⇒ 53 ÷ 57 × 54 × 12 − 125% of 8 = ?

⇒ (53 / 57) × 54 × 12 − 125% of 8 = ?

⇒ (1 / 54) × 54 × 12 − 125% of 8 = ?

⇒ \( {1 \over 25^2}\) × 25² × 12 - 10 = ?

⇒ 1 × 12 - 10 = ?

∴ ? = 2

Given:

(7/132) × (528/9) × √64 ÷ (2/9)

Concept used:

We have to follow the BODMAS rule

Calculation:

7 × (4/9) × 8 ÷ (2/9) = ?

⇒ 7 × (4/9) × 8 × (9/2) = ?

⇒ (28/9) × 36 = ?

⇒ ? = 28 × 4 = 112

∴ The value of ? is 112.

Concept Used: 

Follow the BODMAS rule according to the table given below:

Calculation:

18 + 12 × 6 - 12 ÷ 3 + 77 ÷ 11 = ?

⇒ 18 + 72 - 4 + 7 = ?

⇒ 18 + 79 - 4 = ?

⇒ ? = 97 - 4

∴ 93 will come in place of the question mark ('?').

Concept used:

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

Calculation:

1.6% of 1000 × 2.4% of ? = 288

⇒ 16 × (2.4/100) of ? = 288

⇒ ? = (288 × 100)/(2.4 × 16)

⇒ ? = 750

∴ The value of ? is 750

Concept used:

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

Calculation:

12.5% of 32 + 32.5% of 280 = 92 + (?)

12.5% = 1/8, 

32.5% = 20% + 12.5% = (1/5) + (1/8) = 13/40

Putting the values,

(32/8) + (280/40) × 13 = 81 + (?)

4 + 91 = 81 + (?)

? = 95 - 81 = 14

∴ ? = 14

Alternate Method Fraction value of 12.5% = 1/8

Fraction value of  32.5% = 13/40

12.5% of 32 + 32.5% of 280 = 92 + (?)

⇒ (1/8 × 32) + (13/40 × 280) = 81 + ?

⇒ 4 + 91 = 81 + ?

⇒ 95 = 81 +  ?

⇒ ? = 95 - 81 = 14

Given:

\(56\frac{1}{2}% ;{\rm{of; }}1400{\rm{;}} - {\rm{;}}? = 230\)

Concept used:

We have to follow the BODMAS rule

Calculation:

113/200 of 1400 – ? = 230

⇒ 791 – ? = 230

⇒ ? = 791 – 230 = 561

∴ The value of ? is 561.

Given:

(1/19)(7 × 9 – 12 × 4 + 46 ÷ 2)

Concept used:

We have to follow the BODMAS rule

Calculation:

(1/19)(63 – 48 + 23) = ?

⇒ (1/19)(86 – 48) = ?

⇒ (1/19)(38) = ?

⇒ ? = 2

∴ The value of ? is 2.

Concept:

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. 

Calculation:

Given expression is 

(30% of 230 + 10% of 130) = ? + 34

⇒(69 + 13) = ? + 34 

 ⇒ (82) = ? + 34 

⇒ 82 - 34 = ?

∴ ? = 48

Calculation:

We use the BODMAS rule as follows:

According to the rule ‘Bracket’ should be solved first

⇒ ?% of (19154 - 15644) = 9² + 6²

⇒ ?% of 3510 = 81 + 36

⇒ (?/100) × 3510 = 117

⇒ ? = (117/351) × 10

⇒ ? = 10/3

∴ Required answer is 10/3.

Given:

66.66% of 480 + 37.5% of 832 = 120 + ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

66.66% of 480 + 37.5% of 832 = 120 + ?

⇒ 2/3 × 480 + 3/8 × 832 = 120 + ?

⇒ 320 + 312 = 120 + ?

⇒ ? = 512

∴ The value of ? is 512.

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.

Given expression is

15% of 440 = 25% of ? + 20% of 280

⇒ 66 = 25% of ? + 56

⇒ 10 = 25% of ?

⇒ 10 × 4 = ?

⇒ 40 = ?

⇒ ? = 40

∴ ? = 40

Concept used:

Calculation:

\(4\frac{1}{3} + 2\frac{7}{4} - 5\frac{{11}}{3} = ? + 2\frac{4}{3}\)

⇒ \(4\frac{1}{3} + 2\frac{7}{4} - 5\frac{{11}}{{3}} - 2\frac{4}{3} = ;?\)

⇒ ? = (4 + 2 – 5 – 2) + \(\frac{1}{3} + \frac{7}{4} - \frac{{11}}{3} - \frac{4}{3}\)

⇒ ? = - 1 + \(\frac{{4 + 21 - 44 - 16}}{{12}}\)

⇒ ? = - 1 + (-\(\frac{{35}}{{12}}\))

⇒ ? = -1 - \(\frac{{35}}{{12}}\)

⇒ \(? = ; - \frac{{47}}{{12}} = ; - 3\frac{{11}}{{12}}\)

⇒ Hence, \(; - 3\frac{{11}}{{12}}\) is the correct answer.

Concept Used:

We have to follow the BODMAS rule,

Calculation:

(36 × 15) - 40% of (20)² = ?

⇒ 540 - 40/100 × 400 = ?

⇒ 540 - 160 = ?

⇒ 380 = ?

∴ The value of ? is 380.

Concept Used:

We have to follow the BODMAS rule

Calculation:

25% of 8284 - 18% of 1500 = ?

⇒ 25/100 × 8284 - 18/100 × 1500 = ?

⇒ 2071 - 270 = ?

⇒ ? = 1801

∴ The value of ? is 1801.

Given:

Total sum = Rs. 4350

A receives 25% more than C

B receives 20% more than A

Formula used:

Let the amount received by C = x

Amount received by A = x + 25% of x = 1.25x

Amount received by B = 1.25x + 20% of 1.25x = 1.25x + 0.25x = 1.5x

Calculations:

Total amount = x + 1.25x + 1.5x = 4350

3.75x = 4350

x = 4350 / 3.75

x = 1160

Amount received by B = 1.5x = 1.5 × 1160 = 1740

∴ The amount received by B is Rs. 1740.

Given:

Distance covered by first bus = 320 km

Time taken by first bus = 8 hours

Speed of second bus = 25% more than first bus

Distance to be covered by second bus = 200 km

Formula used:

Speed = Distance / Time

Calculations:

Speed of first bus = 320 km / 8 hours = 40 km/h

Speed of second bus = 40 km/h + 25% of 40 km/h = 40 km/h + 10 km/h = 50 km/h

Time taken by second bus to cover 200 km = Distance / Speed

Time = 200 km / 50 km/h = 4 hours

∴ The time taken by the second bus to cover 200 km is 4 hours.

Given:

Present age of Karan = 25 years

In 5 years, the ratio of age of Karan to Sangeet = 6 : 7

Formula used:

Let the present age of Sangeet = x

After 5 years, age of Karan = 25 + 5 = 30 years

After 5 years, age of Sangeet = x + 5

Calculations:

The ratio of their ages after 5 years = 6 : 7

⇒ (30) / (x + 5) = 6 / 7

⇒ 7 × 30 = 6 × (x + 5)

⇒ 210 = 6x + 30

⇒ 6x = 210 - 30

⇒ 6x = 180

⇒ x = 180 / 6

⇒ x = 30

Present age of Sangeet = 30 years

Age of Sangeet four years ago = 30 - 4 = 26 years

∴ The age of Sangeet four years ago was 26 years.

Calculation

From the given table:

Shop E → Pens = 40, Pencils = 25

So, total in E = 40 + 25 = 65

Let the total number of pens + pencils sold in shop F be x.

According to the ratio:

So, 65/ x = 5/ 6

⇒ 5x = 390

⇒ x = 78

Pens + Pencils in shop F = 78

So, pens in shop F = 78 − 29 = 49

Calculations:

Total number of items sold in shop A = 20 + 35 + 5 = 60

Total number of items sold in shop B = 30 + 50 + 10 = 90

Percentage = (Total items sold in shop A / Total items sold in shop B) × 100

Percentage = (60 / 90) × 100

Percentage = (2 / 3) × 100 = 66.67%

∴ The total number of items sold in shop A is 66.67% of the total number of items sold in shop B.

Calculations:

Number of erasers sold in shop D = 15

Number of scales sold in shop D is 20% more than the number of erasers sold.

Number of scales sold = Number of erasers sold + 20% of number of erasers sold

Number of scales sold = 15 + (20/100) × 15

Number of scales sold = 15 + 3 = 18

∴ The number of scales sold in shop D is 18.

Calculation

Total pens = 20 + 30 + 35 + 45 + 40 = 170

Total pencils = 35 + 50 + 40 + 30 + 25 = 180

Average pens = 170 ÷ 5 = 34

Average pencils = 180 ÷ 5 = 36

Difference = 36 − 34 = 2

Calculations:

Number of pens sold in Shop D = 45

Number of erasers sold in Shop D = 30

Number of pencils sold in Shop D = 15

Total number of items sold in Shop D = Pens + Erasers + Pencils = 45 + 30 + 15 = 90

The total number of items is given as x + 29.

⇒ x + 29 = 90

⇒ x = 90 - 29 = 61

∴ The value of x is 61.

Given:

A can do the work in 18 days

A and B together can do the work in 12 days

Formula used:

Work = LCM of days taken

Efficiency = Work ÷ Time

Time taken by B = Total work ÷ (Efficiency of B)

Calculations:

LCM of 18 and 12 = 36 (since HCF = 6)

⇒ Total work = 36 units

⇒ A’s 1 day work = 36 ÷ 18 = 2 units

⇒ A and B’s 1 day work = 36 ÷ 12 = 3 units

⇒ B’s 1 day work = 3 - 2 = 1 unit

⇒ Time taken by B = 36 ÷ 1 = 36 days

∴ B alone can do the work in 36 days.

Shortcut Trick

Let the Cost Price for A be 100%.

A sold it to B at 20% profit, so Selling Price for A = 120%.

This Selling Price is the Cost Price for B.

Given, 120% = Rs. 30,000.

Value of 100% = (30,000 ÷ 120) × 100 = 25,000.

∴ The correct answer is Rs. 25,000.

Alternate Method

Given: Profit% = 20%, Cost Price for B (which is SP for A) = Rs. 30,000.

Formulas: SP = CP × (100 + P%) ÷ 100

⇒ Let CP for A be x.

⇒ Selling Price for A = x × (100 + 20) ÷ 100

⇒ 30,000 = x × (120 ÷ 100)

⇒ 30,000 = x × 1.2

⇒ x = 30,000 ÷ 1.2

⇒ x = 25,000

∴ The correct answer is Rs. 25,000.

Additional Information

Cost Price and Selling Price Relationship

When an item is sold from one person to another, the Selling Price for the first person becomes the Cost Price for the second person.

Profit Percentage

Profit% is always calculated on the Cost Price unless stated otherwise. Formula: Profit% = (Profit ÷ CP) × 100.

Calculation:

100

100 + 11 = 111

111 + 22 = 133

133 + 44 = 177

177 + 88 = 265

265 + 176 = 441

∴ Wrong answer is 440

Calculation:

\({10^2} + 25 = 125\)

\({12^2} + 25 = 169\)

\({14^2} + 25 = 221\)

\({16^2} + 25 = 281\)

\({18^2} + 25\) = 349

∴ Wrong number is 350

Given:

1150, 1342, 1527, 1705, 1876, 2041

Calculation:

1342 – 1150 = 192

1527 – 1342 = 185

1705 – 1527 = 178

1876 – 1705 = 171

2040 – 1876 = 164 

∴ The wrong term is 2041

The logic followed here is as follows:

⇒ 80/2 = 40

⇒ 40 x 3 = 120

⇒ 120/2 = 60

⇒ 60 x 3 = 180

⇒ 180/2 = 90

⇒ 90 x 3 = 270

So, the wrong term is 181

Hence, the correct answer is 181.

Given:

Total volume of mixture = 108 liters

Ratio of milk to water = 5:4

Milk added = 20 liters

Water added = 36 liters

Formula used:

Milk in the mixture = (Total mixture) × (Ratio of milk / Total ratio)

Water in the mixture = (Total mixture) × (Ratio of water / Total ratio)

Calculations:

Total ratio of milk and water = 5 + 4 = 9

Milk in the mixture = (108 liters) × (5/9) = 60 liters

Water in the mixture = (108 liters) × (4/9) = 48 liters

After adding milk and water:

New amount of milk = 60 + 20 = 80 liters

New amount of water = 48 + 36 = 84 liters

Difference between milk and water in the mixture = 84 - 80 = 4 liters

Y = 4

7Y = 7 × 4 = 28

∴ The value of 7Y is 28.

Given:

Principal (P) = ₹2400

Rate (R) = 20% per annum

Interest (I) = ₹1440

Formula used:

Simple Interest (I) = P × R × T / 100

Calculations:

1440 = 2400 × 20 × T / 100

⇒ 1440 = 480 × T

⇒ T = 1440 / 480

⇒ T = 3 years

∴ 2T = 2 × 3 = 6