Quantitative Aptitude PYQs

Given:

Original Number (O) = 45

Misread Number (M) = 54

Formula used:

Percentage Change = \(\dfrac{(New Value - Original Value)}{Original Value} \times 100\)

Calculation:

Percentage Change = \(\dfrac{(54 - 45)}{45} \times 100\)

⇒ Percentage Change = \(\dfrac{9}{45} \times 100\)

⇒ Percentage Change = \(0.2 \times 100\)

⇒ Percentage Change = 20%

∴ The correct answer is option (2).

Given:

Selling price after 10% discount = ₹360

Formula used:

Original Price (P) = Selling Price / (1 - Discount Rate)

New Selling Price = Original Price × (1 - New Discount Rate)

Calculation:

Let the original price be P.

⇒ P = 360 / (1 - 0.10)

⇒ P = 360 / 0.90

⇒ P = 400

Now, New Selling Price with 20% discount:

⇒ New Selling Price = 400 × (1 - 0.20)

⇒ New Selling Price = 400 × 0.80

⇒ New Selling Price = 320

∴ The correct answer is option 2.

Shortcut Trick

Given:

Diameter of base (d) = 21 cm

Height (h) = 42 cm

Formula used:

Total Surface Area (TSA) of a Cylinder = 2πr(h + r)

Where, r = radius, π = 22/7

Calculation:

Radius (r) = d/2 = 21/2 = 10.5 cm

Total Surface Area (TSA) = 2 × (22/7) × 10.5 × (42 + 10.5)

⇒ TSA = 2 × (22/7) × 10.5 × 52.5

⇒ TSA = 2 × 22 × 78.75

⇒ TSA = 3465 cm²

∴ The correct answer is option (4).

Given:

A policeman chases a thief who is at a distance of 450 metres from him.

Formula Used:

Distance = Speed × Time

Calculation:

Let the time taken for the policeman to catch the thief be t hours.

Relative speed of the policeman with respect to the thief = (12 - 9) km/h = 3 km/h

The initial distance between them is 450 meters = 0.45 km

⇒ Time taken (t) = Distance / Relative speed

⇒ t = 0.45 / 3

⇒ t = 0.15 hours

Distance run by the thief = Thief's speed × Time

⇒ Distance = 9 km/h × 0.15 hours

⇒ Distance = 1.35 km

∴ The correct answer is option 1.

Formula used:

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

Calculation:

Check each option:

1049 only has 1 and 1049 as its divisors, so it's a prime number.

901 = 17 × 53. This is not a prime since it can be divided by 17 and 53.

917 = 7 x 131. This is not a prime since it can be divided by 7 and 131.

1047 = 3 × 349. This is not a prime since it can be divided by 3 and 349.

∴ The correct answer is option (1).

Given:

A loss of 25% gets converted into a profit of 12% when the selling price of an article is increased by Rs. 111.

Formula Used:

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

Loss = Cost Price (CP) - Selling Price (SP)

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

Calculation:

Let the cost price be Rs.

x. Loss of 25% means selling price = 0.75 x x

Profit of 12% means new selling price = 1.12 x x

Given that the difference between new selling price and old selling price is Rs. 111

Therefore, 1.12 x x - 0.75 x x = 111

⇒ 0.37 x x = 111

⇒ x = 111 / 0.37

⇒ x = 300

The cost price of the article is Rs. 300.

Given:

The length of a rectangle is increased by 70%.

The breadth is decreased by 35%.

Formula Used:

New Area = Original Area × (1 + Percentage Increase in Length) × (1 - Percentage Decrease in Breadth)

Calculation:

Let the original length = L and the original breadth = B.

Original Area = L × B

New Length = L × (1 + 70/100) = L × 1.70

New Breadth = B × (1 - 35/100) = B × 0.65

New Area = L × 1.70 × B × 0.65 = L × B × 1.105

Percentage Increase in Area = (New Area - Original Area) / Original Area × 100

Percentage Increase in Area = (1.105 × L × B - L × B) / (L × B) × 100

Percentage Increase in Area = (1.105 - 1) × 100

Percentage Increase in Area = 0.105 × 100

Percentage Increase in Area = 10.5%

The net percentage increase in the area is 10.5%.

Given:

Cost price (CP) of the article = Rs. 1300

Discount = 20%

Cash discount = Rs. 170

Profit = 10%

Formula Used:

Selling Price (SP) = CP × (1 + Profit %)

Marked Price (MP) = SP / (1 - Discount %) + Cash Discount

Calculation:

Selling Price (SP) = 1300 × (1 + 0.10)

⇒ SP = 1300 × 1.10 = Rs. 1430

Marked Price (MP) = (SP + Cash Discount) / (1 - Discount %)

⇒ MP = (1430 + 170) / (1 - 0.20)

⇒ MP = 1600 / 0.80 = Rs. 2000

The marked price of the article is Rs. 2000.

Given:

Expression: \(4\frac{2}{3} + 3\frac{1}{5} - 1\frac{1}{5}\)

Calculation:

\(4\frac{2}{3} + 3\frac{1}{5} - 1\frac{1}{5}\)

⇒ 14/3 + 16/5 - 6/5

Common denominator of 3 and 5 is 15.

⇒ \(\frac{70 + 48- 18}{15}\)

⇒ 100/15 = 20/3 = \(6\frac{2}{3}\)

 

The correct answer is option 2, which is \(6\frac{2}{3}\).

Given:

The ratios are 8/15, 19/20, 23/60, and 27/35.

Formula Used:

To find the ascending order of the ratios, convert each ratio to a decimal.

Calculation:

8/15 = 0.5333

19/20 = 0.95

23/60 = 0.3833

27/35 = 0.7714

Arranging the decimals in ascending order: 0.3833, 0.5333, 0.7714, 0.95

Thus, the ascending order of the ratios is:

23/60, 8/15, 27/35, 19/20

The correct answer is option 3.

Given:

Base of the triangle = L cm.

Height of the triangle = (4L + 7) cm.

Sum of the base and height = 37 cm.

Formula Used:

Area of triangle = (1/2) × Base × Height

Calculation:

Base + Height = 37

L + (4L + 7) = 37

⇒ 5L + 7 = 37

⇒ 5L = 30

⇒ L = 6

Height = 4L + 7 = 4(6) + 7 = 24 + 7

⇒ Height = 31

Area of the triangle = (1/2) × Base × Height

⇒ Area = (1/2) × 6 × 31

⇒ Area = 93 cm²

The area of the triangle is 93 cm².

Given:

Speed of the boat in still water = 13 km/h

Speed of the stream = 4 km/h

Distance to be traveled in the opposite direction to the stream = 63 km

Formula Used:

Time = Distance / Relative Speed

Calculation:

When traveling in the opposite direction to the stream, the relative speed of the boat is reduced by the speed of the stream.

Relative Speed = Speed of the boat - Speed of the stream

Relative Speed = 13 km/h - 4 km/h

Relative Speed = 9 km/h

Time = Distance / Relative Speed

⇒ Time = 63 km / 9 km/h

⇒ Time = 7 hours

The time taken by the boat to go 63 km in the opposite direction to the stream is 7 hours.

Given:

Numbers: 3, 7, 9, -5, 0.25, -3.75

Formula Used:

Average = Sum of all numbers / Total number of values

Calculation:

Sum of numbers = 3 + 7 + 9 + (-5) + 0.25 + (-3.75)

⇒ Sum of numbers = 3 + 7 + 9 - 5 + 0.25 - 3.75

⇒ Sum of numbers = 10.5

Total number of values = 6

Average = Sum of numbers / Total number of values

⇒ Average = 10.5 / 6

⇒ Average = 1.75

The average of the given numbers is 1.75.

Given:

Principal (P) = ₹ 7,81,250

Amount (A) = ₹ 9,13,952

Rate of interest (R) = 4% per annum

Time (T) = ?

Formula used:

Compound Interest formula:

A = P (1 + R/100)^T

Calculation:

Substituting the values:

9,13,952 = 7,81,250 (1 + 4/100)^T

9,13,952 = 7,81,250 × (1.04)^T

Dividing both sides by 7,81,250:

(1.04)^T = 9,13,952 / 7,81,250

(1.04)^T = 1.17

(1.04)T = (1.04)⁴

T = 4

The required time is 4 years.

Given:

42 workers earn Rs. 4,080 in 5 days.

48 workers need to work for 14 days.

Formula Used:

Earnings = (Number of workers × Number of days × Rate per day per worker)

Calculation:

First, find the rate per day per worker.

Rate per day per worker = Total earnings / (Number of workers × Number of days)

Rate per day per worker = 4080 / (42 × 5)

Rate per day per worker = 4080 / 210

Now, calculate the earnings for 48 workers in 14 days.

Earnings = (Number of workers × Number of days × Rate per day per worker)

Earnings = 48 × 14 × (4080 / 210)

Earnings = 48 × 272

Earnings = 13056

The earnings for 48 workers in 14 days is Rs. 13,056.

Given:

Initial income = Rs. 45,000

Ratio of income and expenditure = 9 ∶ 5

Income increases by 40%

Expenditure decreases by 10%

Formula Used:

Final Income = Initial Income × (1 + % Increase in Income)

Final Expenditure = Initial Expenditure × (1 - % Decrease in Expenditure)

Savings = Final Income - Final Expenditure

Calculation:

Initial Income (I) = Rs. 45,000

Let Initial Expenditure be E.

According to the ratio, I/E = 9/5

⇒ E = I × (5/9)

⇒ E = 45000 × (5/9) = 25,000

Final Income = Initial Income × (1 + 40/100)

⇒ Final Income = 45000 × 1.4 = 63,000

Final Expenditure = Initial Expenditure × (1 - 10/100)

⇒ Final Expenditure = 25000 × 0.9 = 22,500

Final Savings = Final Income - Final Expenditure

⇒ Final Savings = 63,000 - 22,500 = 40,500

The final saving is Rs. 40,500.

Given:

The ratio of two numbers = 16 ∶ 19

LCM of the two numbers = 59280

Formula Used:

Let the two numbers be 16k and 19k.

LCM of the two numbers = LCM of 16k and 19k

Calculation:

LCM of 16k and 19k = 59280

Since 16 and 19 are co-prime, their LCM = 16 × 19 × k

⇒ 16 × 19 × k = 59280

⇒ 304k = 59280

⇒ k = 59280 / 304

⇒ k = 195

Therefore, the two numbers are 16k and 19k:

16k = 16 × 195 = 3120

19k = 19 × 195 = 3705

The two numbers are 3120 and 3705.

Given:

The expression to solve is:

\(\frac{1 + 0.000027}{1 - 0.03 + 0.0009}\)

Formula used:

We can use the formula for the sum of cubes:

\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

Solution:

Let a = 1 and b = 0.03. Now, the numerator becomes:

a³ + b³ = 1 + (0.03)³ = (1 + 0.03)(1² - 1 × 0.03 + (0.03)²)

So: \(\frac{1 + 0.000027}{1 - 0.03 + 0.0009}\) 

⇒  \(\frac{(1 + 0.03)(1^2 - 1 × 0.03 + (0.03)^2)}{(1^2 - 1 × 0.03 + (0.03)^2)}\)

⇒ 1 + 0.03

⇒ 1.03

The value of the given expression is 1.03.

Given:

Annual interest rate (R) = 8%

Increase in value = 40%

Formula Used:

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

Where:

P = Principal amount

R = Rate of interest

T = Time in years

Calculation:

Let the principal amount be P.

Increase in value = Simple Interest = 40% of P

⇒ SI = 0.4P

Using the formula for Simple Interest:

⇒ 0.4P = (P × 8 × T) / 100

⇒ 0.4 = (8T) / 100

⇒ 0.4 × 100 = 8T

⇒ 40 = 8T

⇒ T = 40 / 8

⇒ T = 5 years

It will take 5 years for the sum of money to increase its value by 40%.

Given:

Each side of an equilateral triangle is increased by 80%.

Formula used:

Area of an equilateral triangle = (√3 / 4) × side²

Let the initial side length of the triangle be 's'. Then, the initial area is:

Initial Area = (√3 / 4) × s²

If the side length is increased by 80%, the new side length is 1.8s. The new area is:

New Area = (√3 / 4) × (1.8s)² = (√3 / 4) × 3.24s²

Now, the increase in area is:

Increase in Area = New Area - Initial Area

Increase in Area = \(\frac{√3}{4} × 3.24s² - \frac{√3}{4} × s²\)

Increase in Area = \(\frac{√3}{4} × s² \times (3.24 - 1)\) = (√3 / 4) × s² × 2.24

Percentage increase in area = (Increase in Area / Initial Area) × 100

Percentage increase = ((√3 / 4) × s² × 2.24) / ((√3 / 4) × s²) × 100

Percentage increase = 2.24 × 100 = 224%

The area will increase by 224%.