Quantitative Aptitude PYQs

Given:

Rate (r) = 12.5%

Time (t) = 3 years

Amount (A) = ₹13,851

Principal (P) = ?

Formula used:

A = P(1 + r/100)^t

Calculation:

13,851 = P(1 + 12.5/100)³

⇒ 13,851 = P(1 + 0.125)³

⇒ 13,851 = P(1.125)³

⇒ P = ₹9728

∴ The correct answer is option (4).

Given:

A can do the work in 40 days

B can do the work in 60 days

C can do the work in 120 days

Formula used:

Work done = Time taken × Efficiency

Time taken ∝ 1/Efficiency

Calculation:

The efficiency of A is 1/40

The efficiency of B is 1/60

The efficiency of C is 1/120

1^st day work by A = 1/40

2^nd day work by A = 1/60

3^rd day work by A + B + C = 1/40 + 1/60 + 1/120

⇒ (3 + 2 + 1)/120 = 1/20

Work completed in 3 days

⇒ 1/40 + 1/40 + 1/20 = 1/10

Time taken to complete the work

⇒ 3 × 10 = 30 days

∴ In 30 days the work will be completed.

1^st day work by A = 3

2^nd day work by A = 3

3^rd day work by A + B + C = 3 + 2 + 1 = 6

Work done in 3 days is

⇒ 3 + 3 + 6 = 12

Total time required to complete the work

⇒ 120/12 × 3

⇒ 30 days

∴ In 30 days the work will be completed.

Given:

Numbers: 7.012, 4.018, 6.012, 4.048, and 3.91

Formula used:

Average = \(\frac{\text{Sum of all numbers}}{\text{Total count of numbers}}\)

Calculation:

Sum of numbers = 7.012 + 4.018 + 6.012 + 4.048 + 3.91 = 25.0

Total count of numbers = 5

⇒ Average = \(\frac{25.0}{5}\)

⇒ Average = 5

∴ The correct answer is option (3).

Given:

\(\dfrac{1.84}{1.15}\) = ?

Calculation:

Multiply numerator and denominator by 100 to remove decimals

\(\dfrac{1.84}{1.15} = \dfrac{184}{115}\)

⇒ \(\dfrac{184}{115} = \dfrac{8}{5}\)

⇒ \( \dfrac{8}{5} = 1.6 \)

∴ \(\dfrac{1.84}{1.15} = 1.6 \)

Given:

Diameter of large sphere = 20 cm

Diameter of each lead ball = 2 cm

Formula used:

Volume of a sphere = \(\frac{4}{3}\pi r^3\)

Calculation:

Radius of large sphere = \(\frac{20}{2} = 10 , \text{cm}\)

Radius of each lead ball = \(\frac{2}{2} = 1 , \text{cm}\)

Volume of large sphere = \(\frac{4}{3} \times \pi \times 10^3\)

⇒ Volume of large sphere = \(\frac{4}{3} \times \pi \times 1000 = \frac{4000\pi}{3} , \text{cm}^3\)

Volume of each lead ball = \(\frac{4}{3} \times \pi \times 1^3\)

⇒ Volume of each lead ball = \(\frac{4}{3} \times \pi = \frac{4\pi}{3} , \text{cm}^3\)

Number of lead balls = \(\frac{\text{Volume of large sphere}}{\text{Volume of each lead ball}}\)

⇒ Number of lead balls = \(\frac{\frac{4000\pi}{3}}{\frac{4\pi}{3}}\)

⇒ Number of lead balls = \(\frac{4000}{4} = 1000\)

∴ The correct answer is option (1).

Given:

Diameter of the sphere = 28 cm

Radius of the sphere (r) = 28 ÷ 2 = 14 cm

Formula used:

Curved Surface Area (CSA) of a hemisphere = 2 × π × r²

Calculation:

CSA = 2 × π × r²

⇒ CSA = 2 × (22/7) × 14²

⇒ CSA = 2 × (22/7) × 196

⇒ CSA = (2 × 22 × 196) ÷ 7

⇒ CSA = 1232 cm²

∴ The correct answer is option (3).

Given:

Total votes = 40,000

Votes received by Ram = 48%

Votes received by Ramesh = 36%

Formula used:

Votes received by Ganesh = Total votes - (Votes received by Ram + Votes received by Ramesh)

Calculations:

⇒ Votes received by Ram = 19,200

⇒ Votes received by Ramesh = 14,400

⇒ Votes received by Ganesh = 40,000 - (19,200 + 14,400)

⇒ Votes received by Ganesh = 40,000 - 33,600 = 6,400

∴ The correct answer is option (3).

Given:

SP = ₹5,862

Profit% = 20%

New SP = ₹5,000

Formula used:

CP = \(\dfrac{SP}{(1+\frac{Profit%}{100})}\)

New Profit/Loss% = \(\dfrac{New\ SP - CP}{CP} \times 100\)

Calculation:

CP = \(\dfrac{5862}{(1+\frac{20}{100})}\)

⇒ CP = \(\dfrac{5862}{1.2}\)

⇒ CP = ₹4,885

New Profit/Loss% = \(\dfrac{5000 - 4885}{4885} \times 100\)

⇒ New Profit% = \(\dfrac{115}{4885} \times 100\)

⇒ New Profit% = 2.4%

∴ The correct answer is option (2).

Given:

Rate (R) = 5%

Time = 12/5 %

Amount = Rs. 1120

Formula used:

SI = PRT / 100

Amount = Principal + SI

Calculation:

Amount = Principal + [PRT / 100] 

⇒ 1120 = P + [(P × 5 × 12) / (100 × 5)]

⇒ 1120 = P[1 + (3/25)]

⇒ 1120 = 28P / 25

⇒ 40 = P / 25

⇒ P = 40 × 25 = 1000

∴ The principal is Rs. 1000.

Given:

x : y = 2 : 3

y : z = 4 : 7

z : w = 7 : 3

Formula used:

To find combined ratio x : y : z : w, align and equalize the common terms (y, z).

Calculation:

Equalize y in both x : y and y : z

x : y = 2 : 3 → Multiply by 4 → x : y = 8 : 12

y : z = 4 : 7 → Multiply by 3 → y : z = 12 : 21

Combine x : y : z

x : y : z = 8 : 12 : 21

Equalize z in both y : z and z : w

z : w = 7 : 3 → Multiply by 3 → z : w = 21 : 9

Combine x : y : z : w

x : y : z : w = 8 : 12 : 21 : 9

∴ The correct answer is option (3).

Given:

Expression:

Calculation:

Numerator: 7 ÷ (7 × 7)

⇒ 7 ÷ 49

⇒ 1 / 7

Denominator: (7 ÷ 7) × 7

⇒ 1 × 7

⇒ 7

Now, the expression becomes:

⇒ (1 / 7) ÷ 7

⇒ 1 / 49

∴ The simplified value of the expression is 1/49.

Given:

Initial expenditure = 80%

Income increases by 30% 

Expenditure increases by 10%

Formula Used:

Savings = Income - Expenditure

Percentage increase in savings = \(\frac{\text{New Savings - Old Savings}}{\text{Old Savings}} \times 100\)

Calculations:

Initial income = ₹100 (Assumed)

Initial expenditure = 80% of income = ₹80

Initial savings = Income - Expenditure = ₹100 - ₹80 = ₹20

Income increases by 30% = ₹100 × 1.30 = ₹130

Expenditure increases by 10% = ₹80 × 1.10 = ₹88

New savings = ₹130 - ₹88 = ₹42

Old savings = ₹20

Percentage increase in savings:

⇒ \(\frac{42 - 20}{20} \times 100\)

⇒ \(\frac{22}{20} \times 100\) = 110%

∴ The correct answer is option (2).

Given:

Marked Price (MP) = ₹7,600

Discount = 15%

Gain = 25%

Formula used:

Selling Price (SP) = MP × (1 - Discount/100)

Cost Price (CP) = SP / (1 + Gain/100)

Calculation:

SP = 7600 × (1 - 15/100)

⇒ SP = 7600 × 0.85 = ₹6,460

CP = 6460 / (1 + 25/100)

⇒ CP = 6460 / 1.25 = ₹5,168

∴ The correct answer is option (1).

Given:

Find the number of prime numbers less than 40.

Formula used:

A prime number is a number greater than 1 that has no divisors other than 1 and itself.

Calculation:

Prime numbers less than 40 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

⇒ Total prime numbers = 12

∴ The correct answer is option (1).

Given:

Speed of missile = 1152 km/h

Time = 1 second

Formula used:

Distance = Speed × Time

Speed in m/s = Speed in km/h × \(\frac{1000}{3600}\)

Calculations:

Speed in m/s = 1152 × \(\frac{5}{18}\) = 320 m/s

Distance traveled in 1 second = Speed × Time

⇒ Distance = 320 × 1 = 320 m

∴ The correct answer is option (2).

Given:

A shopkeeper gains 35% after allowing a discount of 15% on the marked price of an article.

Formula used:

Selling Price (SP) = Marked Price (MP) × (1 - Discount/100)

Cost Price (CP) = SP / (1 + Profit%/100)

Profit% = [(Selling Price - Cost Price) / Cost Price] × 100

Calculations:

Let the marked price (MP) = ₹100

Discount given = 15%

⇒ Selling Price (SP) = MP × (1 - Discount/100)

⇒ SP = 100 × (1 - 15/100) = ₹85

Profit% = 35%

⇒ Cost Price (CP) = SP / (1 + Profit%/100)

⇒ CP = 85 / (1 + 35/100)

⇒ CP = 85 / 1.35 = ₹62.96 

Now, if the article is sold at the marked price (₹100) with no discount:

⇒ New SP = ₹100

⇒ Profit = New SP - CP

⇒ Profit = ₹100 - ₹62.96 = ₹37.04

⇒ Profit% = (Profit / CP) × 100

⇒ Profit% = (37.04 / 62.96) × 100 = 58.82%

∴ The correct answer is option (1).

Given:

Two shelves sold for ₹650 each

Profit on one = 30%

Loss on other = 20%

New selling price for both = ₹875 each

Formula used:

Profit% = \(\dfrac{Profit}{Cost Price} \times 100 \)

Loss% = \(\dfrac{Loss}{Cost Price} \times 100 \)

Total CP = CP₁ + CP₂, Total SP = SP₁ + SP₂

Calculation:

Let CP of shelf 1 = x

Profit = 30% ⇒ SP = 650

⇒ \(650 = x + \dfrac{30}{100}x = x \times \dfrac{130}{100} \)

⇒ \(x = \dfrac{650 \times 100}{130} = 500\)

Let CP of shelf 2 = y

Loss = 20% ⇒ SP = 650

⇒ \(650 = y - \dfrac{20}{100}y = y \times \dfrac{80}{100}\)

⇒ \(y = \dfrac{650 \times 100}{80} = 812.5 \)

Total CP = 500 + 812.5 = 1312.5

New total SP = 875 × 2 = 1750

Profit = 1750 - 1312.5 = 437.5

Profit% = \(\dfrac{437.5}{1312.5} \times 100 \) = 33%

∴ The correct answer is 33% (rounded to nearest integer).

Given:

The sum of the radius of the base and the height of a solid cylinder (r + h) = 42 m

Total surface area of the cylinder = 3696 m²

Formula used:

Total surface area of a cylinder = 2πr(r + h)

Volume of a cylinder = πr²h

Calculations:

Total surface area = 2πr(r + h)

⇒ 3696 = 2 × (22/7) × r × 42

⇒ r × 42 = 588

⇒ r = 14

Now, r + h = 42

⇒ 14 + h = 42

⇒ h = 28

Volume of the cylinder = πr²h

⇒ Volume = (22/7) × 14² × 28

⇒ Volume = (22/7) × 196 × 28

⇒ Volume = 17248 m³

∴ The correct answer is option (2).

Given:

Savings = ₹20,000

Spending = ₹6,000

Formula used:

Percentage decrease = (Spending / Savings) × 100

Calculation:

Percentage decrease = (6,000 / 20,000) × 100

⇒ Percentage decrease = 30%

∴ The correct answer is option (3).

Given:

The length of the rectangle is increased by 5%, and its breadth is decreased by 5%.

Formula used:

Percentage change in area = (x - y - (x × y)/100) %

Where:

x = Percentage increase in length = 5%

y = Percentage decrease in breadth = 5%

Calculation:

Percentage change in area = (5 - 5 - (5 × 5)/100)%

⇒ Percentage change in area = (5 - 5 - 25/100)%

⇒ Percentage decreasee in area = -0.25%

∴ The correct answer is option (1).