Quantitative Aptitude PYQs

Given:

6 years hence, age of A is 22 years.

Present age of A + B is 48 years.

C is 10 years younger than B.

Formula used:

Let the present age of A be x, the present age of B be y, and the present age of C be z.

Calculation:

6 years hence, the age of A = 22 years, so present age of A is:

x + 6 = 22

⇒ x = 22 - 6 = 16 years

The present age of A + B is 48 years:

x + y = 48

Substitute x = 16 into this equation:

16 + y = 48

⇒ y = 48 - 16 = 32 years

C is 10 years younger than B, so the present age of C is:

z = y - 10 = 32 - 10 = 22 years

∴ The present age of C is 22 years.

Given:

A scores 4 marks less than B.

B got 12 marks less than passing marks.

A’s marks is 80% of the passing marks.

Formula used:

Let the passing marks be P.

Let the marks scored by B be B marks, and A’s marks will be A marks.

Calculation:

From the given information:

A = B - 4 (A scores 4 marks less than B)

B = P - 12 (B got 12 marks less than passing marks)

A = 0.8 × P (A’s marks is 80% of the passing marks)

Now substitute the value of A from the second equation into the third equation:

B - 4 = 0.8 × P

Substitute B = P - 12 into this equation:

(P - 12) - 4 = 0.8 × P

P - 16 = 0.8 × P

Now, solve for P:

P - 0.8P = 16

0.2P = 16

P = 16 / 0.2 = 80

The passing marks are 80. Now, substitute P = 80 into the equation for B’s marks:

B = P - 12 = 80 - 12 = 68

∴ The marks scored by B is 68.

Given:

Principal amount (P) = Rs. 9,000

Time (T) = 7 years

Ratio between total interest and principal = 7 : 10

Formula used:

Simple Interest (SI) = (P × R × T) / 100

Calculation:

We are given that the ratio of the total interest (SI) to the principal amount (P) is 7 : 10. This means:

SI / P = 7 / 10

Substitute P = 9000 into the equation:

SI / 9000 = 7 / 10

SI = (7 / 10) × 9000

SI = 6300

∴ The simple interest is Rs. 6300.

Given:

Shirts sold by A = 76

Shirts sold by B = 20

Trousers sold by C = 22

Trousers sold by D = 88

Trousers sold by E = 90

Calculation:

Sum of shirts sold by A and B = 76 + 20 = 96

Sum of trousers sold by C, D, and E = 22 + 88 + 90 = 200

The ratio of the sum of shirts sold by A and B to the sum of trousers sold by C, D, and E is:

Ratio = 96 / 200 = 24 / 50 = 12 / 25

∴ The ratio is 12 : 25.

Given:

Jeans sold by shop B = 90

Trousers sold by shop B = 75

Calculation:

To find the percentage, we use the formula:

Percentage = (Jeans sold by shop B / Trousers sold by shop B) × 100

Percentage = (90 / 75) × 100 = 1.2 × 100 = 120%

∴ Jeans sold by shop B is 120% of trousers sold by shop B.

Calculation:

Shirts sold by all shops:

Shop A: 76, Shop B: 20, Shop C: 75, Shop D: 22, Shop E: 44

Total shirts sold = 76 + 20 + 75 + 22 + 44 = 237

Jeans sold by all shops:

Shop A: 48, Shop B: 90, Shop C: 45, Shop D: 110, Shop E: 25

Total jeans sold = 48 + 90 + 45 + 110 + 25 = 318

Difference between shirts sold and jeans sold = 318 - 237 = 81

∴ The difference between shirts sold by all shops and jeans sold by all shops is 81.

Given:

Shirts sold by B = 20

Shirts sold by E = 44

Trousers sold by D = 88

Calculation:

Total shirts sold by B and E = 20 + 44 = 64

Now, find the difference between the total shirts sold by B and E and trousers sold by D:

Difference = 88  - 64 = -24

∴ Shirts sold by B and E are 24 less than trousers sold by D.

Calculation:

Total shirts sold = 76 + 20 + 75 + 22 + 44 = 237

Number of shops = 5

Average number of shirts sold = Total shirts sold / Number of shops

Average = 237 / 5 = 47.4

∴ The average number of shirts sold by all shops together is 47.4.

Given:

Tom can complete the work in 8 days.

Tom and Jerry together can complete the work in 2\(2\over3\) days.

Calculation:

Total work = LCM( 8, 8/3) = 8 units

Efficiency of Tom = 8/8 = 1 unit per day

Efficiency of Tom and Jerry = (8 × 3)/8 = 3 unit per day

Efficiency of Jerry = 3 - 1 = 2 unit per day

Double work = 8 × 2 = 16 units

Days required by Jerry alone to complete double work = 16/2 = 8 days

∴ Option 3 is the correct answer.

Given:

The speed of the boat to the speed of the stream is in the ratio 7 : 2.

The boat covers a certain distance downstream in 1 hour.

Let the speed of the boat be 7x and the speed of the stream be 2x.

Calculation:

The effective speed of the boat downstream is the sum of the boat's speed and the stream's speed:

Speed downstream = 7x + 2x = 9x

It is given that the boat covers a certain distance downstream in 1 hour. So, the distance covered downstream is:

Distance = Speed × Time = 9x × 1 = 9x

Now, to cover the same distance upstream, the effective speed of the boat is the difference between the boat's speed and the stream's speed:

Speed upstream = 7x - 2x = 5x

The time taken to cover the same distance upstream is:

Time = Distance / Speed = 9x / 5x = 9 / 5 hours

Converting the time to minutes (since 1 hour = 60 minutes):

Time in minutes = (9 / 5) × 60 = 108 minutes

∴ The time taken by the boat to cover the same distance upstream is 108 minutes.

Calculation:

(150) × 2 ÷ (12 ÷ 0.5) × 2 × 1.2 = ?

(150) × 2 ÷ 24 × 2.4 = ?

(150) × 2/24 × 2.4 = ?

15 × 2/24 × 24 = ?

30

∴ Option 4 is the correct answer.

Calculation:

\({(18 × ?)}÷120 × 60 + 48 = 54\)

⇒ (18 × ?) ÷ 120 × 60 = 54 - 48

⇒ (18 × ?) ÷ 120 × 60 = 6

⇒ (18 × ?) ÷ 120 = 6 ÷ 60

⇒ (18 × ?) ÷ 120 = 1/10

⇒ (18 × ?) = 1/10 × 120

⇒ 18 × ? = 12

⇒ ? = 12 ÷ 18

⇒ ? = 2/3 

∴ The value of '?' is 2/3 ​.

Calculation:

(5 × 27 × 2) ÷ ? = 108 

270 ÷ ? = 108 

270 ÷ 108 = ?

? = 5/2

? = 2(1/2)

∴ Option 1 is the correct answer.

Calculation:

12.5 + 155.5 + 120 - 130 = 125 + ?

First, simplify the left side:

12.5 + 155.5 = 168

168 + 120 = 288

288 - 130 = 158

Now, the equation becomes:

158 = 125 + ?

Subtract 125 from both sides:

? = 158 - 125

? = 33

∴ The value of '?' is 33.

Calculation:

33\(\frac{1}{3}\) ÷ 150 × 80 + ? = 32\(\frac{7}{9}\)

⇒ 100/3 ÷ 150 × 80 + ? = 295/9

⇒ 100/3 × 1/150 × 80 + ? = 295/9

⇒ 2/3 × 1/3 × 80 + ? = 295/9

⇒ 160/9 + ? = 295/9

⇒ ? = 295/9 - 160/9

⇒ ? = 135/9 = 15

∴ Option 1 is the correct answer.

Calculation:

85 ÷ 100 × ? × 15 = 5763 

⇒ 85/100 × ? × 15 = 5763 

⇒ 17/20 × ? × 15 = 5763 

⇒ 17/4 × ? × 3 = 5763 

⇒ ? = 5763 × 4/51

⇒ ? = 113 × 4

⇒ ? = 452

Calculation:

1600 ÷ (24)2 × 1.2 = ?

1600 ÷ 576 × 1.2 = ?

1600/576 × 1.2 = ?

? = 400/144 × 1.2

? = 40/144 × 12

? = 40/12

? = 10/3 = 3(1/3)

∴ Option 3 is the correct answer.

Calculation:

\(\sqrt{(1536/512× ?-6)} = 12\)

\(\sqrt{(3× ?-6)} = 12\)

(3 × ? - 6) = 144

3 × ?  = 150

? = 50

∴ Option 4 is the correct answer.

Calculation:

\(\frac{1}{4}\times \frac{45}{150}\times\sqrt[3]{343}=? \)

\(\frac{1}{4}\times \frac{3}{10}\times7=? \)

? = 21/40

∴ Option 1 is the correct answer.

Calculation:

72 × 105 ÷ ? + 63 = 567 

⇒ 72 × 105 ÷ ? = 567 - 63

⇒ 72 × 105 ÷ ? = 504

⇒ 7560 ÷ ? = 504

⇒ ? = 7560 ÷ 504

⇒ ? = 15

∴ The value of '?' is 15.