Quantitative Aptitude PYQs

Given:

Simple interest rate for 3 years.

Interest difference if rate is 5% higher = Rs. 270. Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Calculation:

Let the principal be P.

Rate difference = 5%

Time = 3 years

Interest difference = Rs. 270

Using the formula for simple interest:

⇒ (P × 5 × 3) / 100 = 270

⇒ P × 15 / 100 = 270

⇒ P × 0.15 = 270

⇒ P = 270 / 0.15

⇒ P = 1800

The sum invested was Rs. 1800.

Given:

Principal (P) = Rs. 2,400

Amount (A) = Rs. 3,650.10

Time (T) = 3 years

Formula Used:

Compound Interest Formula: \(A = P \left(1 + \frac{R}{100}\right)^T\)

Calculation:

\(3,650.10 = 2,400 \left(1 + \frac{R}{100}\right)^3\)

Dividing both sides by 2,400:

\(\frac{3,650.10}{2,400} = \left(1 + \frac{R}{100}\right)^3\)

⇒ 1.520875 = \(\left(1 + \frac{R}{100}\right)^3\)

Taking the cube root of both sides:

⇒ 1 + \(\frac{R}{100}\) = \(\sqrt[3]{1.520875}\)

⇒ 1 + \(\frac{R}{100}\) = 1.146

Subtracting 1 from both sides:

⇒ \(\frac{R}{100}\) = 0.146

Multiplying both sides by 100:

⇒ R = 0.146 × 100

⇒ R = 14.6% ≈ 15%

The yearly rate of compound interest is 15%.

Given:

A can finish the work in 15 days.

B can finish the work in 20 days.

B starts the work on 1 October, and they work on alternate days.

Formula Used:

Total work = Time × Efficiency 

Calculation:

Total work = LCM(15, 20) = 60 units

Efficiency of A = 60/15 = 4

Efficiency of B = 60/20 = 3

If B starts work on 1 October then A starts work on 2 October,

Work done in 2 days = 3 + 4 = 7 units

Multiply both sides by 8

8 × 2 days = 8 × 7 units

Work complete in 16 days = 56 units

After 17 days = 56 + 3 = 59 units

On 18 day A complete the remaining 1 unit of work.

Therefore, the work will be finished on Sat Oct 18 2025.

The correct answer is option 3.

Given:

Expression: [0.7 - {4.3 - 3.6 - (6.1 - 4.7 - 2.3)}]

Formula Used:

We will use the BODMAS/BIDMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) to solve the expression.

Calculation:

[0.7 - {4.3 - 3.6 - (6.1 - 7)}]

[0.7 - {4.3 - 3.6 + 0.9}]

[0.7 - {5.2 - 3.6}]

[0.7 - 1.6]

• 0.9 = - 9/10

∴ Option 1 is the correct answer.

Given:

The ratio of the numbers of boys and girls in a school is 6 ∶ 5.

25% of the boys are scholarship holders.

36% of the girls are scholarship holders.

Formula Used:

Percentage of students who do not get scholarships = 100% - Percentage of students who get scholarships.

Calculation:

Given, ratio of number of boys and girls in a school is 6 ∶ 5.

Let the number of boys and girls be 6a and 5a respectively. Where a is any constant

Given, 25% of the boys and 36% of the girls are scholarship holders.

Total number of boys who are not getting scholarship = 75% of 6a = 4.5a

Total number of girls who are not getting scholarship = 64% of 5a = 3.2a

Total number of students not getting scholarship = 4.5a + 3.2a = 7.7a

% of students not getting the scholarship = \(\frac{7.7a}{11a} \times 100\) = 70%

∴ Option 4 is the correct answer.

Given:

The average of two numbers is 24.

The average of three other numbers is 29.

Formula Used:

Average = (Sum of all numbers) / (Total numbers)

Calculation:

Let the sum of the first two numbers be S₁.

S₁ / 2 = 24

⇒ S₁ = 24 × 2 = 48

Let the sum of the other three numbers be S₂.

S₂ / 3 = 29

⇒ S₂ = 29 × 3 = 87

Total sum of all five numbers = S₁ + S₂

Total sum of all five numbers = 48 + 87 = 135

Total number of numbers = 5

Average = Total sum of all five numbers / Total number of numbers

Average = 135 / 5

⇒ Average = 27

The average of these five numbers is 27.

Given:

In 2001, production decreased by 30%.

In 2002, production increased by 25%.

Formula Used:

Resulting change = Initial production × (1 - Decrease %) × (1 + Increase %)

Calculation:

Let the initial production be 100 units.

Production after a 30% decrease in 2001:

Production = 100 × (1 - 0.30)

Production = 100 × 0.70

Production = 70 units

Production after a 25% increase in 2002:

Production = 70 × (1 + 0.25)

Production = 70 × 1.25

Production = 87.5 units

Resulting change in production = 87.5 - 100

Resulting change = -12.5 units

Percentage change = (-12.5 / 100) × 100%

Percentage change = -12.5%

Therefore, the resulting change in production over these two years is a decrease of 12.5%.

Given:

Marked price = Cost price + 65% of Cost price

Discount allowed = 35%

Formula Used:

Selling Price = Marked Price - Discount

Profit Percentage = (Selling Price - Cost Price) / Cost Price × 100

Calculation:

Let the Cost Price (CP) be 100.

Marked Price (MP) = CP + 65% of CP

⇒ MP = 100 + 65% of 100

⇒ MP = 100 + 65 = 165

Discount = 35% of MP

⇒ Discount = 35% of 165

⇒ Discount = (35/100) × 165 = 57.75

Selling Price (SP) = MP - Discount

⇒ SP = 165 - 57.75 = 107.25

Profit = SP - CP

⇒ Profit = 107.25 - 100 = 7.25

Profit Percentage = (Profit / CP) × 100

⇒ Profit Percentage = (7.25 / 100) × 100

⇒ Profit Percentage = 7.25%

The percentage of his profit is 7.25%.

Given:

Radius of the spherical ball (r) = 14 cm

Rate of painting = Rs. 10 per cm²

Formula Used:

Surface Area of Sphere = 4πr²

Cost of Painting = Surface Area × Rate

Calculation:

Surface Area of Sphere = 4πr²

⇒ Surface Area = 4 × (22/7) × 14²

⇒ Surface Area = 4 × (22/7) × 196

⇒ Surface Area = 4 × 22 × 28

⇒ Surface Area = 2464 cm²

Cost of Painting = 2464 × 10 = 24640

The cost of painting the spherical ball is Rs. 24,640.

Given:

Width of cloth = 6 m

Radius of the base of the tent = 6 m

Height of the tent = 8 m

Formula Used:

Surface Area of the cone = πrl

Length of the cloth required = (Surface Area) / (Width of cloth)

Calculation:

First, find the slant height (l) using the Pythagorean theorem:

⇒ l = \(\sqrt{r^2 + h^2}\)

⇒ l = \(\sqrt{6^2 + 8^2}\)

⇒ l = \(\sqrt{36 + 64}\) = \(\sqrt{100}\)

⇒ l = 10 m

Now, calculate the surface area of the cone:

Surface Area = πrl

⇒ Surface Area = \(\frac{22}{7} × 6 × 10\)

⇒ Surface Area = \(\frac{1320}{7}\)

Length of cloth required:

Length = (Surface Area) / (Width of cloth)

⇒ Length = \(\frac{ \frac{1320}{7}}{6}\)

⇒ Length = \(\frac{220}{7}\) m = 31\(\frac{3}{7}\)

The length of cloth required is 31\(\frac{3}{7}\) m.

Given:

Cash price = Rs. 39,300

Down payment = Rs. 7,450

Interest rate = 20% per annum (compounded annually)

Calculation:

Amount to be financed = Rs. 39,300 - Rs. 7,450 = Rs. 31,850

Let the amount of each installment be 'a'.

The total amount paid in installments will be the sum of the installments with compound interest.

The formula for compound interest is:

Amount = P(1 + r)ⁿ, where P is the principal, r is the rate of interest, and n is the number of years.

The installment amount 'a' for 3 years with annual compounding is given by:

⇒ 31,850 = a / (1 + 20/100) + a / (1 + 20/100)² + a / (1 + 20/100)³

⇒ 31,850 = a / 1.2 + a / 1.44 + a / 1.728

⇒ 31,850 = a (1 / 1.2 + 1 / 1.44 + 1 / 1.728)

Calculate the sum inside the parentheses:

1 / 1.2 = 0.8333

1 / 1.44 = 0.6944

1 / 1.728 = 0.5787

⇒ 31,850 = a (0.8333 + 0.6944 + 0.5787)

⇒ 31,850 = a (2.1064)

⇒ a = 31,850 / 2.1064

⇒ a = 15,120

Therefore, the amount of each installment is Rs. 15,120.

Given:

Selling price of the item = Rs. 1,500

Loss = 20%

Desired gain = 10%

Formula Used:

Cost Price (CP) = Selling Price / (1 - Loss%)

Selling Price for desired gain = Cost Price × (1 + Gain%)

Calculation:

Loss = 20% = 20/100 = 0.20

Selling Price (SP) = Rs. 1,500

⇒ Cost Price (CP) = 1,500 / (1 - 0.20)

⇒ CP = 1,500 / 0.80

⇒ CP = 1,875

Gain = 10% = 10/100 = 0.10

⇒ Selling Price for 10% gain = 1,875 × (1 + 0.10)

⇒ Selling Price for 10% gain = 1,875 × 1.10

⇒ Selling Price for 10% gain = 2,062.50

Therefore, the amount for which he should sell the item to gain 10% is Rs. 2,062.50.

Given:

Two prime numbers: p and q.

Formula Used:

Average of two numbers = (p + q)/2

Calculation:

We need to find the average of p and q.

Average = (p + q)/2

⇒ Average = (p + q)/2

The average of p and q is (p + q)/2.

Given:

Diameter of the sphere = 10 cm

Formula Used:

Volume of a sphere = (4/3)πr³

Where,

r = radius of the sphere

Calculation:

Radius (r) = Diameter / 2 = 10 cm / 2 = 5 cm

Now, convert the radius into metres: 5 cm = 0.05 m

Volume = (4/3)π(0.05)³

⇒ Volume = (4/3)π(0.000125)

⇒ Volume = (4/3) × π × 1/8000

⇒ Volume = (4/24000)π

⇒ Volume = (1/6000)π m³ = \(\frac{(\pi)}{(6)} × 10^{(-3)}\)

The volume of the sphere is \(\frac{(\pi)}{(6)} × 10^{(-3)}\).

Given:

The price of the article is fixed at 24% above the cost of production.

Discount allowed on the fixed price is 15%.

Profit made is Rs. 27. Formula Used:

Selling Price (SP) = Fixed Price - Discount

Profit = Selling Price - Cost of Production

Calculation:

Let the cost of production be Rs.

x. Fixed Price = x + 24% of x

Fixed Price = x + 0.24x = 1.24x

Discount = 15% of Fixed Price

Discount = 0.15 × 1.24x = 0.186x

Selling Price = Fixed Price - Discount

Selling Price = 1.24x - 0.186x = 1.054x

Profit = Selling Price - Cost of Production

→ 27 = 1.054x - x

→ 27 = 0.054x

→ x = 27 / 0.054

→ x = 500

The cost of production of the article is Rs. 500.

Given:

Diameter of the hemisphere = 14 cm

Radius of the hemisphere (r) = 14/2 = 7 cm

π = 22/7

Formula Used:

Volume of a hemisphere = (2/3) π r³

Calculation:

Volume of the hemisphere

Volume = (2/3) π r³

π = 22/7

r = 7 cm

→ Volume = (2/3) × (22/7) × 7³

→ Volume = (2/3) × (22/7) × 343

→ Volume = (2/3) × 22 × 49

→ Volume = (2 × 22 × 49)/3

→ Volume = 2156/3

The volume of the hemisphere is 2156/3 cm³.

Given:

The ratio of two numbers is 5∶7 and their difference is 48.

Calculation:

Let the two numbers be 5x and 7x.

The difference between the numbers is given by 7x - 5x = 48.

7x - 5x = 48

→ 2x = 48

→ x = 48 / 2

→ x = 24

The smaller of the two numbers is 5x.

5x = 5 × 24

5x = 120

The smaller of the two numbers is 120.

Given:

A can complete the work in 30 days

B can complete the work in 40 days

They work together for 8 days

Formula used:

Total Work = Time × Efficiency

Calculation:

LCM(30,40) = 120 (Total work units)

Work done per day: A = 120/30 = 4, B = 120/40 = 3

Work done together per day = 4 + 3 = 7

Work done in 8 days = 8 × 7 = 56

Remaining work = 120 - 56 = 64

A alone completes 4 units/day

Days required = 64/4 = 16

∴ A will finish the remaining work in 16 days.

Given:

The number to be expressed as the product of two coprime numbers = 480.

Formula Used:

If two numbers a and b are coprime and their product is n, then any such n can be written as a × b where a and b are coprime.

Calculation:

Prime factorization of 480:

480 = 2⁵ × 3 × 5

To form two coprime numbers, we need to group the prime factors such that each group is coprime with the other. The possible groupings are:

The 4 pairs of coprime factors (a, b) whose product is 480 are:

1. (1, 480), where HCF of {1 and 480} = 1
2. (3, 160), where HCF of {3 and 160} = 1 3. (5, 96), where HCF of {5 and 96} = 1 4. (15, 32), where HCF of {15 and 32} = 1

These are the 4 ways to write 480 as the product of two numbers which are coprime to each other.

The correct answer is option 4.

Given:

Percentage of voters who cast votes = 80%

Percentage of invalid votes = 5%

Votes received by a candidate = 5,700

Votes received = 75% of valid votes

Formula used:

Total valid votes = Total votes cast - Invalid votes

Let total enrolled voters be X.

Total votes cast = \(\dfrac{80}{100} \times X\)

Invalid votes = \(\dfrac{5}{100} \times (\dfrac{80}{100} \times X)\)

Valid votes = Total votes cast - Invalid votes

A candidate’s votes = 75% of valid votes

Calculation:

Total votes cast:

⇒ \(\dfrac{80}{100} \times X = 0.8X \)

Invalid votes:

⇒ \(\dfrac{5}{100} \times 0.8X = 0.04X\)

Valid votes:

⇒ \(0.8X - 0.04X = 0.76X\)

Given that 75% of valid votes = 5,700:

⇒ \( \dfrac{75}{100} \times 0.76X = 5700 \)

⇒ \(0.57X = 5700\)

⇒ \(X = \dfrac{5700}{0.57}\)

⇒ X = 10,000

∴ The total number of voters enrolled in the election is 10,000.