Quantitative Aptitude PYQs

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