Quantitative Aptitude PYQs

Given:

Speed = 84 km/h

Time = 45 seconds

Formula used:

Distance = Speed × Time

Calculations:

Speed in m/s = 84 × (5/18)

Distance = Speed × Time

⇒ Distance = 84 × (5/18) × 45

⇒ Distance = 1050 metres

∴ The correct answer is option (2).

Given:

56 workers earn ₹4,050 in 5 days.

Find how much 48 workers will earn in 14 days.

Formula used:

Earnings ∝ Number of Workers × Number of Days

Calculation:

Let the earnings of 48 workers in 14 days be ₹x.

Earnings ratio:

(56 × 5) : (48 × 14) = 4050 : x

⇒ (56 × 5) / (48 × 14) = 4050 / x

⇒ x = (4050 × 48 × 14) / (56 × 5)

⇒ x = (4050 × 672) / 280

⇒ x = 9,720

∴ The correct answer is option (3).

Given:

The sum of two numbers = 72

Their difference = (1/9) of their sum

 

Calculation:

Let the two numbers be x and y.

x + y = 72

x - y = (1/9) × 72

⇒ x - y = 8

Add the two equations:

(x + y) + (x - y) = 72 + 8

⇒ 2x = 80

⇒ x = 40

Subtract the two equations:

(x + y) - (x - y) = 72 - 8

⇒ 2y = 64

⇒ y = 32

Now calculate the LCM of 40 and 32:

Prime factorization of 40 = 2³ × 5

Prime factorization of 32 = 2⁵

LCM = 2⁵ × 5

⇒ LCM = 32 × 5 = 160

∴ The correct answer is option (4).

Given:

Principal (P) = ₹1,264

Rate of interest (R) = 5% p.a.

Time (T) = 3 years

Formula used:

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

Amount (A) = P + SI

Calculations:

SI = (1264 × 5 × 3) / 100

⇒ SI = (1264 × 15) / 100

⇒ SI = ₹189.60

Amount (A) = P + SI

⇒ A = 1264 + 189.60

⇒ A = ₹1,453.60

∴ The correct answer is option (3).

Given:

The cloth required to cover the curved area is double the cloth required to cover the flat areas of a cylinder.

Formula used:

Total Surface Area (TSA) of Cylinder = 2πr² + 2πrh

Curved Surface Area (CSA) of Cylinder = 2πrh

Flat Areas (Top + Bottom) = 2πr²

Given, CSA = 2 × Flat Areas

Calculations:

2πrh = 2 × 2πr²

⇒ h = 2r

⇒ Ratio of height to radius = h : r = 2 : 1

∴ The correct answer is option (1).

Given:

P, Q, R, and S are prime numbers such that P + Q + R + S = 45 and P < Q < R < S.

Formula used:

Use the concept of parity (odd/even):

Sum of four odd numbers = even; 45 is odd ⇒ one prime must be even

The only even prime number is 2

Calculations:

Since P is the smallest prime and sum of primes is 45 (odd), one of them must be even

⇒ P = 2

Now calculate: \(P^4 + 2P \)

⇒ 2⁴ + 2 × 2 = 16 + 4

⇒ 20

∴ The value of P4 + 2P is 20.

Given:

x = 0.35

y = 6/5

Formula used:

The value of the expression: x × y ÷ (100x - 30y) × (y / 2.1) + 6 / y

Calculation:

Expression: x × y ÷ (100x - 30y) × (y / 2.1) + 6 / y

⇒ x = 0.35, y = 6/5 = 1.2

⇒ x × y = 0.35 × 1.2 = 0.42

⇒ 100x = 100 × 0.35 = 35

⇒ 30y = 30 × 1.2 = 36

⇒ 100x - 30y = 35 - 36 = -1

⇒ y / 2.1 = 1.2 / 2.1 = 0.5714

⇒ x × y ÷ (100x - 30y) = 0.42 ÷ -1 = -0.42

⇒ -0.42 × (y / 2.1) = -0.42 × 0.5714 = -0.24

⇒ 6 / y = 6 / 1.2 = 5

⇒ Final value = -0.24 + 5 = 4.76

∴ The correct answer is option (4).

Given:

Ankit is twice as old as Reena.

Reena is three times older than Sanjana.

Calculation:

Let the age of Sanjana be x.

Reena's age = 3x.

Ankit's age = 2 × Reena's age = 2 × 3x = 6x.

Ratio = Ankit's age : Reena's age : Sanjana's age.

Ratio = 6x : 3x : x

⇒ Ratio = 6 : 3 : 1

∴ The correct answer is option (2).

Given:

Population after 2 years = 8,00,865

Rate of increase (r) = 11% per annum

Time (t) = 2 years

Formula used:

Population after t years (A) = P × (1 + r/100)^t

Where, P = Population 2 years ago

Calculation:

8,00,865 = P × (1 + 11/100)²

⇒ 8,00,865 = P × (111/100)²

⇒ 8,00,865 = P × (111 × 111)/(100 × 100)

⇒ P = 6,50,000

∴ The correct answer is option (2).

Given:

The numbers are: 15, 27, 34, 48

Formula used:

Average = (Sum of numbers) / (Total number of terms)

Calculation:

Sum of numbers = 15 + 27 + 34 + 48 = 124

⇒ Average = 124 / 4

⇒ Average = 31

∴ The correct answer is option (4).

Given:

Numbers: 9, 8.1, 0.27, 0.09

Formula used:

L.C.M of the fraction = L.C.M of numerator/H.C.F of denominator

Calculation:

To calculate the LCM, convert all numbers to their fractional forms:

9 = 9/1, 8.1 = 81/10, 0.27 = 27/100, 0.09 = 9/100

LCM of ( 9/1, 81/10, 27/100, 9/100)

LCM of numarators = 9, 81, 27, 9 = 81

HCF of denominators = 1, 10, 100 = 1

LCM of fractions = 81/1 = 81

∴ The correct answer is option (2).

Given:

Diameter of the hemisphere = 8 cm

Radius (r) = Diameter/2 = 8/2 = 4 cm

Formula used:

Volume of hemisphere = (2/3) × π × r³

Calculation:

Volume = (2/3) × π × (4)³

⇒ Volume = (2/3) × π × 64

⇒ Volume = (128/3) × π

⇒ Volume = \(42\frac{2}{3}\pi\) cm³

∴ The correct answer is option (2).

Given:

The numbers to be multiplied are 0.325 and 1.0302.  

Formula used:

The number of digits after the decimal in the product is equal to the sum of the number of decimal places in both numbers.

Calculation:

When we multiply the numbers 0.325 and 1.0302, the result is 0.334815. 

⇒ So, the digits after the decimal point are 6, as we don't count the 0 after the decimal in the last.

∴ The correct answer is option (4).

Given:

Numbers: (1)/(3), (2)/(3), (2)/(9), (3)/(12)

Formula used:

HCF of fractions = (HCF of numerators)/(LCM of denominators)

Calculation:

Numerators: 1, 2, 2, 3

Denominators: 3, 3, 9, 12

HCF of numerators: 1

LCM of denominators: LCM of 3, 3, 9, and 12

Prime factorization:

3 = 3

9 = 3 × 3

12 = 3 × 2 × 2

LCM = 3 × 3 × 2 × 2 = 36

⇒ HCF of fractions = \(\frac{1}{36}\)

∴ The correct answer is option (1).

Given:

Profit at selling price = 7¹/₂%

Additional selling price = ₹1,430

Profit at increased selling price = 35%

Formula used:

Selling price = Cost price × (1 + Profit%/100)

Cost price = Selling price / (1 + Profit%/100)

Calculation:

Let the cost price be ₹x.

For the first selling price:

Selling price = x × (1 + 7¹/₂/100)

⇒ Selling price = x × (1 + 0.075) = x × 1.075

For the increased selling price:

New selling price = x × (1 + 35/100)

⇒ New selling price = x × 1.35

The difference between the two selling prices is ₹1,430:

⇒ New selling price - Original selling price = ₹1,430

⇒ x × 1.35 - x × 1.075 = ₹1,430

⇒ x(1.35 - 1.075) = ₹1,430

⇒ x = ₹1,430 / 0.275 = ₹5,200

∴ The correct answer is option 1 (₹5,200).

Given:

Installment (I) = ₹960

Rate of compound interest (r) = 5%

Number of years (n) = 2

Formula used:

Formula for present value of installments:

Principal (P) = \(\dfrac{I}{(1+\frac{r}{100})^1} + \dfrac{I}{(1+\frac{r}{100})^2}\)

Calculations:

P = \(\dfrac{960}{(1+\frac{5}{100})^1} + \dfrac{960}{(1+\frac{5}{100})^2}\)

⇒ P = \(\dfrac{960}{1.05} + \dfrac{960}{(1.05)^2}\)

⇒ P = \(\dfrac{960}{1.05} + \dfrac{960}{1.1025}\)

⇒ P = 914.29 + 870.74

⇒ P = 1,785.03

∴ The correct answer is option (1).

Given:

Discount = 20%

Selling Price (SP) = ₹500

Formula used:

SP = MP × (1 - Discount/100)

Calculation:

500 = MP × (1 - 20/100)

⇒ 500 = MP × (1 - 0.2)

⇒ 500 = MP × 0.8

⇒ MP = ₹625

∴ The correct answer is option (3).

Given:

Initial ratio of incomes of A, B, and C = 3 : 5 : 4

Formula used:

New income of A = 3 × Initial income of A

New income of B = Initial income of B

New income of C = 2 × Initial income of C

New ratio = New income of A : New income of B : New income of C

Calculation:

Let the initial incomes of A, B, and C be 3x, 5x, and 4x respectively.

New income of A = 3 × 3x = 9x

New income of B = 5x

New income of C = 2 × 4x = 8x

New ratio = 9x : 5x : 8x

⇒ New ratio = 9 : 5 : 8

∴ The correct answer is option (2).

Given:

Farida's salary in the social sector (new salary) = ₹27,000

Percentage decrease in salary = 28%

Formula used:

New Salary = Previous Salary × (1 - Percentage Decrease/100)

Calculation:

27,000 = Previous Salary × (1 - 28/100)

⇒ 27,000 = Previous Salary × 0.72

⇒ Previous Salary = 37,500

∴ The correct answer is option (2).

Given:

Principal (P) = ₹1,800

Time (t) = 3 years

Difference in Simple Interest (SI) = ₹40

Formula used:

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

Difference in SI = P × (R₁ - R₂) × T / 100

Calculations:

₹40 = ₹1,800 × (R₁ - R₂) × 3 / 100

⇒ ₹40 = ₹5,400 × (R₁ - R₂) / 100

⇒ ₹4,000 = ₹5,400 × (R₁ - R₂)

⇒ (R₁ - R₂) = ₹4,000 / ₹5,400

⇒ (R₁ - R₂) = 20/27%

∴ The correct answer is option (1).