Quantitative Aptitude PYQs

Given:

Average of 10 numbers = 16.2

Numbers reduced by = 3

Formula used:

New average = Old average - Reduction per number

Calculation:

New average = 16.2 - 3

⇒ New average = 13.2

∴ The new average is 13.2.

Given:

Marked price (MP) = 12% above cost price (CP)

Sold half the stock at MP

Sold one-quarter at 12% discount on MP

Sold one-quarter at 30% discount on MP

Formula used:

Selling Price (SP) = Cost Price (CP) + Profit

Calculation:

Let CP = 100

Marked Price (MP) = 100 + 12% of 100

⇒ MP = 100 + 12

⇒ MP = 112

Selling half at MP:

⇒ SP₁ = 112 × 1/2

⇒ SP₁ = 56

Selling one quarter at a discount of 12% on MP:

⇒ SP₂ = 112 × (1 - 0.12) × 1/4

⇒ SP₂ = 112 × 0.88 × 1/4

⇒ SP₂ = 24.64

Selling the rest at a discount of 30% on MP:

⇒ SP₃ = 112 × (1 - 0.30) × 1/4

⇒ SP₃ = 112 × 0.70 × 1/4

⇒ SP₃ = 19.6

Total SP:

⇒ Total SP = SP₁ + SP₂ + SP₃

⇒ Total SP = 56 + 24.64 + 19.6

⇒ Total SP = 100.24

Total gain:

⇒ Gain = Total SP - CP

⇒ Gain = 100.24 - 100

⇒ Gain = 0.24

Gain percentage:

⇒ Gain % = (Gain / CP) × 100

⇒ Gain % = (0.24 / 100) × 100

⇒ Gain % = 0.24%

∴ The correct answer is option (1).

Given:

Amount in 2 years (A₂) = ₹1250

Amount in 5 years (A₅) = ₹2000

Time difference = 5 - 2 = 3 years

Formula used:

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

Difference in amounts = Simple Interest for 3 years

Rate (R) = (SI × 100) / (P × T)

Calculation:

Difference in amounts: ₹2000 - ₹1250 = ₹750

Simple Interest for 3 years = ₹750

Principal (P) = Amount in 2 years - SI for 2 years

SI for 2 years = ₹750 × (2 / 3) = ₹500

P = ₹1250 - ₹500 = ₹750

Rate (R):

R = (SI × 100) / (P × T)

⇒ R = (750 × 100) / (750 × 3)

⇒ R = 100 / 3

⇒ R = 33.33%

∴ The rate of interest is 33.33% per annum.

Given:

Numbers: 47, 95, 187

Formula used:

To find the greatest number that leaves the same remainder when dividing multiple numbers, we use the GCD (Greatest Common Divisor) of the differences between the numbers.

Calculation:

First, find the differences:

95 - 47 = 48

187 - 95 = 92

187 - 47 = 140

Now, find the GCD of 48, 92, and 140.

48 = 2 × 2 × 2 × 2 × 3

92 = 2 × 2 × 23

140 = 2 × 2 × 5 × 7

Common factors: 2 × 2 = 4

⇒ GCD = 4

∴ The correct answer is option 1.

Given:

Distance = 1800 m

Time = 12 minutes

Formula used:

Speed (km/hr) = (Distance in km) / (Time in hours)

Calculation:

Distance in km = 1800 / 1000 = 1.8 km

Time in hours = 12 / 60 = 0.2 hours

⇒ Speed = 1.8 / 0.2

⇒ Speed = 9 km/hr

∴ The correct answer is  9 km/hr.

Given:

Thickness of each coin = 0.2 cm

Diameter of each coin = 2 cm ⇒ Radius (rcoin) = 1 cm

Height of the cylinder (hcylinder) = 12 cm

Diameter of the cylinder = 5 cm ⇒ Radius (rcylinder) = 2.5 cm

Formula used:

Volume of a cylinder = πr2h

Number of coins = Volume of cylinder / Volume of one coin

Calculation:

Volume of one coin:

Vcoin = πr2h

⇒ Vcoin = π × (1)2 × 0.2 = 0.2π cm3

Volume of the cylinder:

Vcylinder = πr2h

⇒ Vcylinder = π × (2.5)2 × 12

⇒ Vcylinder = π × 6.25 × 12 = 75π cm3

Number of coins:

Number of coins = Vcylinder / Vcoin

⇒ Number of coins = 75π / 0.2π

⇒ Number of coins = 375

∴ The number of coins required is 375.

Given:

The difference between the CI and SI on a certain sum of money for 3 years at 4% per annum is Rs. 152.

Formula used:

CI - SI for 3 years = P × (r/100)² × [(300 + r)/100]

Calculations:

152 = P × (4/100)² × [(300 + 4)/100]

⇒ 152 = P × (16/10000) × (304/100)

⇒ 152 = P × (16/10000) × (304/100)

⇒ 152 = P × (16 × 304) / 1000000

⇒ 152 = P × 4864 / 1000000

⇒ 152 = P × 0.004864

⇒ P = 152 / 0.004864

⇒ P = 31,250

∴ The correct answer is option (3).

Formula used:

Let the original fraction be x/y.

New fraction = (1.17x) / (0.88y) = 39 / 44

Calculation:

(1.17x) / (0.88y) = 39 / 44

⇒ (1.17x × 44) / (0.88y × 44) = (39 × 44) / (44 × 44)

⇒ (1.17 / 0.88) × (x / y) = 39 / 44

⇒ x / y = (39 × 0.88) / (44 × 1.17)

⇒ x / y = 0.88 / 1.17

⇒ x / y = 2 / 3

∴ The original fraction is 2/3.

Given:

p/q = 0.5

Formula used:

(3p - q) / (3p + q)

Calculation:

p/q = 0.5

⇒ p = 0.5q

(3p - q) / (3p + q)

⇒ (3(0.5q) - q) / (3(0.5q) + q)

⇒ (1.5q - q) / (1.5q + q)

⇒ 0.5q / 2.5q

⇒ 0.5 / 2.5

⇒ 1 / 5

∴ The correct answer is option (2).

Given:

The salaries of P, Q, and R are in the ratio 3 ∶ 4 ∶ 6.

R's salary is ₹15,000 more than that of P.

Formula used:

Let the salaries be 3x, 4x, and 6x respectively for P, Q, and R.

6x - 3x = ₹15,000

Calculation:

6x - 3x = ₹15,000

⇒ 3x = ₹15,000

⇒ x = ₹5,000

Q's salary = 4x

⇒ Q's salary = 4 × ₹5,000

⇒ Q's salary = ₹20,000

∴ The correct answer is option 2.

Given:

The product of two numbers = 8427.

The HCF of these numbers = 53.

Formula Used:

Product of two numbers = HCF x LCM

Calculation:

Let the numbers be 53a and 53b.

Then, product of the numbers = (53a) x (53b) = 8427

⇒ 53² x a x b = 8427

⇒ 2809 x a x b = 8427

⇒ a x b = 3

Since a and b are factors of 3, possible pairs (a, b) are (1, 3) and (3, 1).

Hence, the two numbers can be 53 x 1 = 53 and 53 x 3 = 159.

The greater number is 159.

Given:

Three successive discounts of 15%, 10%, and 8%.

Formula Used:

Single equivalent discount, k = 1 - (1 - d₁) × (1 - d₂) × (1 - d₃)

Calculation:

Let the original price be P.

After the first discount of 15%, the price becomes P × (1 - 0.15).

After the second discount of 10%, the price becomes P × (1 - 0.15) × (1 - 0.10).

After the third discount of 8%, the price becomes P × (1 - 0.15) × (1 - 0.10) × (1 - 0.08).

So the effective price after all three discounts is:

P × (1 - 0.15) × (1 - 0.10) × (1 - 0.08)

P × 0.85 × 0.90 × 0.92

⇒ P × 0.85 × 0.90 × 0.92 = P × 0.702

The single equivalent discount k is:

⇒ k = 1 - 0.702

⇒ k = 0.298

Therefore, the single equivalent discount is 29.62%.

The correct answer is option 3.

Given:

Half of the clothes sold at 30% profit.

Half of the remaining clothes sold at 20% loss.

The rest sold at cost price.

Formula Used:

Net Profit or Loss Percentage = (Total Profit or Loss) / (Total Cost Price) × 100

Calculation:

Let the total cost price be 100 units.

Clothes sold at 30% profit:

⇒ Cost Price = 50 units

⇒ Selling Price = 50 × 1.30 = 65 units

Remaining clothes = 50 units

Half of the remaining clothes sold at 20% loss:

⇒ Cost Price = 25 units

⇒ Selling Price = 25 × 0.80 = 20 units

Remaining clothes sold at cost price:

⇒ Cost Price = 25 units

⇒ Selling Price = 25 units

Total Selling Price = 65 + 20 + 25 = 110 units

Total Cost Price = 100 units

Net Profit = Total Selling Price - Total Cost Price

⇒ Net Profit = 110 - 100 = 10 units

Net Profit Percentage = (10) / (100) × 100

⇒ Net Profit Percentage = 10%

The correct answer is option 2: Profit 10%

The monthly income of a person is Rs. 45,000. If his income is increased by 25%, then find his new monthly income (in Rs.). ,55500,58250,56250,11250,,3

Given:

Monthly income of the person = Rs. 45,000

Income increase percentage = 25%

Formula Used:

New Income = Old Income + (Old Income × Increase Percentage / 100)

Calculation:

Old Income = 45,000

Increase Percentage = 25%

Increase Amount = 45,000 × 25 / 100

⇒ Increase Amount = 45,000 × 0.25

⇒ Increase Amount = 11,250

New Income = 45,000 + 11,250

⇒ New Income = 56,250

The new monthly income is Rs. 56,250.

Given:

Area of the first triangle = 420 cm²

Base of the first triangle = 60 cm

Area of the second triangle = 1500 cm²

Base of the second triangle = 7.5 cm

Formula Used:

Area of a triangle = (1/2) × base × height

Ratio of heights = height of the first triangle / height of the second triangle

Calculation:

For the first triangle:

Area = (1/2) × base × height

420 = (1/2) × 60 × height

⇒ 420 = 30 × height

⇒ height = 420 / 30

⇒ height = 14 cm

For the second triangle:

Area = (1/2) × base × height

1500 = (1/2) × 7.5 × height

⇒ 1500 = 3.75 × height

⇒ height = 1500 / 3.75

⇒ height = 400 cm

Ratio of heights = height of the first triangle / height of the second triangle

Ratio = 14 / 400

⇒ Ratio = 7 / 200

The ratio of the height of the first triangle to that of the second triangle is 7 ∶ 200.

Calculation:

The given expression,

⇒\(\frac{0.0203 \times 2.92}{0.7 \times 0.0365 \times 2.9}\)

Remove the decimal from numerator and denominator:

⇒\(\frac{203 \times 292\times 10^6}{7 \times 365 \times 29\times 10^6}\)

Cancel out the terms from numerator and denominator:

⇒\(\frac{292}{365}\)

⇒0.8

Option 1 is the correct answer.

Given:

We need to find the value of n for which 3ⁿ - 2ⁿ and 3ⁿ + 2ⁿ are prime numbers.

Formula Used:

To find n such that both 3ⁿ - 2ⁿ and 3ⁿ + 2ⁿ are prime numbers.

Calculation:

We need to check the options one by one:

For n = 4:

3⁴ - 2⁴ = 81 - 16 = 65 (not prime)

3⁴ + 2⁴ = 81 + 16 = 97 (prime)

For n = 2:

3² - 2² = 9 - 4 = 5 (prime)

3² + 2² = 9 + 4 = 13 (prime)

For n = 5:

3⁵ - 2⁵ = 243 - 32 = 211 (prime)

3⁵ + 2⁵ = 243 + 32 = 275 (not prime)

For n = 3:

3³ - 2³ = 27 - 8 = 19 (prime)

3³ + 2³ = 27 + 8 = 35 (not prime)

The correct answer is option 2

n = 2

Given:

The average of 10 terms = 50

The average of the first 5 terms = 45

Formula Used:

Average = Sum of terms / Number of terms

Calculation:

Sum of all 10 terms = 50 × 10

Sum of all 10 terms = 500

Sum of the first 5 terms = 45 × 5

Sum of the first 5 terms = 225

Sum of the remaining 5 terms = 500 - 225

Sum of the remaining 5 terms = 275

Average of the remaining 5 terms = 275 / 5

⇒ Average of the remaining 5 terms = 55

The average of the remaining 5 terms is 55.

Sample question: A person takes a loan of Rs. 4,000 for 3 years at 8% per annum compound interest. He repaid Rs. 2,000 in each of the first and second years. The amount he should pay at the end of the third year to clear all his debt is: 1)Rs. 500.20 2)Rs. 567.12 3)Rs. 546.05 4)Rs. 525.34 5) The correct answer is option 3

Given:

Principal (P) = Rs. 4,000

Rate (R) = 8% per annum

Time (T) = 3 years

Repayment in the first year = Rs. 2,000

Repayment in the second year = Rs. 2,000

Formula Used:

Compound Interest Formula: A = P(1 + R/100)ⁿ

Calculation:

1. Amount at the end of the first year:

A₁ = 4000 × (1 + 8/100)¹

⇒ A₁ = 4000 × 1.08

⇒ A₁ = 4320

After repaying Rs. 2,000:

Remaining Amount = 4320 - 2000

⇒ Remaining Amount = 2320

2. Amount at the end of the second year:

A₂ = 2320 × (1 + 8/100)¹

⇒ A₂ = 2320 × 1.08

⇒ A₂ = 2505.60

After repaying Rs. 2,000:

Remaining Amount = 2505.60 - 2000

⇒ Remaining Amount = 505.60 3. Amount at the end of the third year:

A₃ = 505.60 × (1 + 8/100)¹

⇒ A₃ = 505.60 × 1.08

⇒ A₃ = 546.05

The amount to be paid at the end of the third year to clear all the debt is Rs. 546.05.

Given:

Total distance = 90 km

Total time = 9 hours

Speed on foot = 9 km/hr

Speed on bicycle = 18 km/hr

Formula Used:

Distance = Speed × Time

Total Distance = Distance on foot + Distance on bicycle

Total Time = Time on foot + Time on bicycle

Calculation:

Let the distance traveled on foot be d km.

Then, the distance traveled on bicycle = 90 - d km.

Time taken on foot = d / 9 hours

Time taken on bicycle = (90 - d) / 18 hours

Total Time = d / 9 + (90 - d) / 18

Given Total Time = 9 hours

⇒ d / 9 + (90 - d) / 18 = 9

⇒ (d)/(9) + (90 - d)/(18) = 9

Multiplying by 18 throughout:

⇒ 2d + 90 - d = 162

⇒ 2d - d = 162 - 90

⇒ d = 72

The distance he travels on foot is 72 km.