Quantitative Aptitude PYQs

Calculation:

17/8 × ?/51 × 4/9 = 20/27

⇒ (17 × ? × 4) / (8 × 51 × 9) = 20 / 27

⇒ (68 × ?) / (3684) = 20 / 27

⇒ 68 × ? = (20 × 3684) / 27

⇒ 68 × ? = 73680 / 27

⇒ 68 × ? = 2720

⇒ ? = 2720 / 68

⇒ ? = 40

∴ The value of '?' is 40.

Calculation:

2252 + 1176 + ? + 75 = 3503

3503 + ? = 3503

⇒ ? = 3503 - 3503

⇒ ? = 0

∴ The value of '?' is 0.

Calculation:

\( (?)^3 + 600 = 725 \)

First, subtract 600 from both sides to isolate the cube term:

\( (?)^3 = 725 - 600 \)

\( (?)^3 = 125 \)

Now, take the cube root of both sides to solve for '?':

\( ? = \sqrt[3]{125} \)

\( ? = 5 \)

∴ The value of '?' is 5.

Calculation:

? × 12 × 3/4 + 120 = 786

First, subtract 120 from both sides:

? × 12 × 3/4 = 786 - 120

? × 12 × 3/4 = 666

Now, simplify the left side:

? × (12 × 3/4) = 666

? × 9 = 666

Now, divide both sides by 9:

? = 666 ÷ 9

? = 74

∴ The value of '?' is 74.

Calculation:

345.5 + 125 + 112 - 34 = ?

First, add the numbers on the left side:

345.5 + 125 = 470.5

470.5 + 112 = 582.5

Now, subtract 34:

582.5 - 34 = 548.5

∴ The value of '?' is 548.5.

Given:

The perimeter (circumference) of the circle is 66 meters, which is 3/4^th of the actual perimeter of the circle.

Formula used:

Perimeter (Circumference) of circle = 2πr

Let the actual perimeter of the circle be C, and we know that:

3C/4 = 66 

Calculation:

First, find the actual perimeter C by multiplying both sides of the equation by 4/3:

C = 66 × 4/3 = 88 m

Now, use the formula for the perimeter of a circle, C = 2π r, to find the radius:

88 = 2 × 22/7 × r

r = (88 × 7)(2 × 22) = 616/44= 14 m

Now, use the formula for the area of a circle, A = πr², to find the area:

A = 22/7 × 14²

A = 22/7 × 196 = 4312/7 = 616 m²

∴ The area of the circle is 616 m².

Given:

Population of the town in 2022 = 4520

Population of the town in 2023 = 5650

Formula used:

Percentage increase in population = (New Population - Old Population) / Old Population × 100

Calculation:

Percentage increase = (5650 - 4520) / 4520 × 100

Percentage increase = 1130 / 4520 × 100

Percentage increase = 0.25 × 100 = 25%

∴ The percentage increase in population is 25%.

Given:

Average of A, B, and C = 60

The ratio of the sum of A and B to C is 7:2.

A is 20 more than B.

Calculation:

Average of A, B, and C = (A + B + C) / 3 = 60

A + B + C = 60 × 3 = 180

Also, we are given that (A + B) / C = 7 / 2. Therefore:

A + B = (7 / 2) × C

From A = B + 20, substitute this into the equation A + B = (7 / 2) × C:

(B + 20 + B) = (7 / 2) × C

2B + 20 = (7 / 2) × C

Now, we also know that A + B + C = 180. Substitute A = B + 20 into this equation:

(B + 20) + B + C = 180

2B + 20 + C = 180

C = 180 - 2B - 20

C = 160 - 2B

Now substitute C = 160 - 2B into the equation 2B + 20 = (7 / 2) × C:

2B + 20 = (7 / 2) × (160 - 2B)

2B + 20 = 560 - 7B

2B + 7B = 560 - 20

9B = 540

B = 540 / 9 = 60

∴ The value of B is 60.

Given:

The income of A in 2014 = 12% more than the income of B in 2017

Calculation:

The income of A in 2014 = 25 lakhs × (100 + 12)%

⇒ 25 × (112/100)

⇒ 112/4

⇒ Rs. 28 lakhs

The total income of A in 2016 and 2018 together = 15 + 20

⇒ Rs. 35 lakhs

The total income of A in 2014 and B in 2020 together = 28 + 10

⇒ Rs. 38 lakhs

The required ratio = 35 : 38

∴ The ratio between the income of A in 2016 and 2018 together and that of A in 2014 and B in 2020 together will be 35 ∶ 38.

Given:

The income of B in 2019 = Rs. 25 lakhs

The profit of B in 2019 = 20% of total Income

Formula Used:

Profit = Income - Expnediture 

Calculation:

Income = 25,00,000

Profit is 20% of total income of B in 2019.

⇒ Profit = 25,00,000 × (20/100)

⇒ Profit = 5,00,000

⇒ Expenditure = 25,00,000 - 5,00,000

⇒ Expenditure = 20,00,000

∴ The expenditure of B in 2019 will be Rs. 20 lakhs.

Given:

The ratio of income and expenditure of A in 2017 = 5 ∶ 2

The saving of B in 2019 = 27% more than the saving of A in 2017

Formula Used:

Income = Expenditure + Saving

Calculation:

Let the income and expenditure of A in 2017 be Rs. 5x and Rs. 2x.

According to the question,

5x = Rs. 10 lakhs

⇒ x = Rs. 2 lakhs

⇒ 2x = Rs. 4 lakhs

The expenditure of A in 2017 = Rs. 4 lakhs

The saving of A in 2017 = Income - Expenditure

⇒ 10 - 4

⇒ Rs. 6 lakhs

The saving of B in 2019 = 6 × (100 + 27)%

⇒ 6 lakhs × (127/100)

⇒ Rs. 7.62 lakhs

Hence the expenditure of B in 2019 = Income - Saving

⇒ (25 - 7.62) lakhs

⇒ 17.38 lakhs

∴ The expenditure of B in 2019 will be Rs. 17.38 lakhs.

Given:

The income of A in 2016 now = 30% more than the initial income of A in 2016 

The income of A in 2017 now = 20% more than the initial income of A in 2017

The income of A in 2019 now = 40% more than the initial income of A in 2019

Calculation:

The income of A in 2016 now = 15 × (100 + 30)%

⇒ {15 × (130/100)} lakhs

The income of A in 2017 now = 10 × (100 + 20)%

⇒ {10 × (120/100)} lakhs

The income of A in 2019 now = 20 × (100 + 40)%

⇒ {20 × (140/100)} lakhs

The ratio of income of A in 2016 and 2017 now = {15 × (130/100)}/{10 × (120/100)}

⇒ 13 : 8 ---(1)

The ratio of income of A in 2017 and 2019 now = {10 × (120/100)}/{20 × (140/100)}

⇒ 3 : 7 ---(2)

Now multiply by 3 in equation (1) and 8 in equation (2) respectively,

The ratio of income of A in 2016 and 2017 now = 39 ∶ 24

The ratio of income of A in 2017 and 2019 now = 24 ∶ 56

Hence the ratio of income of A in 2016, 2017 and 2019 now = 39 ∶ 24 ∶ 56

∴ The ratio of income of A in 2016, 2017 and 2019 now will be 39 ∶ 24 ∶ 56.

Given:

The profit of A in 2016 = 20% of Total Income

The ratio of expenditure of A in 2016 to that of B in 2017 = 4 ∶ 5

Formula Used:

Expenditure = Income × {100/(100 + Profit )}

Income = Expenditure + Saving

Calculation:

Profit of A in 2016 = 20% of 15 lakh = 3 lakh

So, Expenditure of A in 2016 = 15 - 3 = 12 lakh

Let the expenditure of A in 2016 and B in 2017 be Rs. 4x and Rs. 5x

Now, 4x = 12 lakhs

⇒ x = 3 lakhs

⇒ 5x = 15lakhs

The expenditure of B in 2017 = Rs. 15 lakhs

The saving of B in 2017 = Income - Expenditure

⇒ (25 - 15) lakhs

⇒ 10 lakhs

∴ The saving of B in 2017 will be Rs. 10 lakhs.

Given:

Zoya's friend's profit = Rs. 5,584

Calculation:

Investment ratio of Zoya and her friend = 3:2 (based on amount and time).

Friend’s profit = (2 / 5) × Total profit = 5,584

Total profit = 5,584 × (5 / 2) = 13,960

Zoya's profit = (3 / 5) × 13,960 = 8,376

Profit difference = Zoya's profit - Friend's profit = 8,376 - 5,584 = 2,792

∴ The profit difference between Zoya and her friend is Rs. 2,792.

Given:

The initial ratio of milk and water is 5 : 2.

10 litres of water is added to the mixture.

The difference between the quantity of milk and water becomes 20 litres.

Let the initial quantity of the mixture be X litres.

Calculation:

Since the ratio of milk to water is 5:2, we can say:

Milk = (5 / 7) × X

Water = (2 / 7) × X

After adding 10 litres of water, the new quantity of water becomes:

Water = (2 / 7) × X + 10

The difference between the amount of milk and water is given as 20 litres:

Milk - Water = 20

Substitute the values for milk and water:

(5 / 7) × X - [(2 / 7) × X + 10] = 20

Now, simplify the equation:

(5 / 7) × X - (2 / 7) × X - 10 = 20

(3 / 7) × X - 10 = 20

Now, add 10 to both sides:

(3 / 7) × X = 30

Now, multiply both sides by 7/3:

X = (30 × 7) / 3

X = 70

∴ The initial quantity of the mixture is 70 litres.

Given:

Initial ratio of milk to water = 11 : 3

26 liters of milk is added, then another 13 liters of milk is added.

Final ratio of milk to water = 12 : 3

Let:

Initial quantity of milk = 11x liters

Initial quantity of water = 3x liters

26 liters + 13 liters = 39 liters

Final milk = 11x + 39

(11x + 39) : 3x = 12 : 3

(11x + 39) / 3x = 4

11x + 39 = 12x

39 = 12x - 11x

x = 39

Initial milk = 11x = 11 x 39 = 429 liters

The initial quantity of milk in the mixture was 429 liters.

Bull's work rate = 1 field / 5 days = 1 / 5 field/day

Buffalo's work rate =1 field / 10 days = 1 / 10 field/day

3 Bulls = 3 × 1 / 5 = 3 / 5 field/day

2 Buffaloes = 2 × 1 / 10 = 2 / 10 = 1 / 5 field/day

Total work rate = (3 / 5) + (1 / 5) = 4 / 5 field/day

Time = Total Work / Work Rate =  1field / (4/5 field/day) = 5 / 4 days = 1.25 days

Thus, the correct answer is 1.25 days.

Let the greater number be x.

Then, the smaller number = (x/2) + 13 

Given:

Difference = x - [(x/2) + 13] = 30

x - (x/2) - 13 = 30

x/2 = 30 + 13

x/2 = 43

x = 86

Thus, the correct answer is 86.

Given:

Perimeter (P) = 40 cm

Difference between length and breadth = l - b = 6 cm

Perimeter formula for a rectangle:

P = 2(l + b)

Substituting the given perimeter:

2l + b = 40

l + b = 20.......................(Equation 1)

Given difference:

l - b = 6............................(Equation 2)

Add Equation 1 and Equation 2:

(l + b) + (l  - b) = 20 + 6

2l = 26

l = 13cm

Substitute l = 13 into Equation 1:

13 + b = 20

b = 7cm

A = l × b = 13 × 7 = 91cm²

Thus, the correct answer is 91 cm²

Books sold by P = 32

Books sold by S = 50

Difference = 50 (S) - 32 (P) = 18

Percentage increase = 18 / 32 × 100% = 56.25%

Thus, the correct answer is 56.25%.