Quantitative Aptitude PYQs

Follow BODMAS rule to solve this question, as per the order given below, 

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, 

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next, 

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated, 

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated 

630 ÷ 9 × {(118 - 106) + 3} = ?

⇒ 630 ÷ 9 × {12 + 3} = ?

⇒ 630 × 1/9 × 15 = ?

⇒ 70 × 15 = ?

∴ ? = 1050

Shortcut Trick

Rate = 10% → Multiplying factor for 1 year = 1.1

For 3 years, Amount = Principal × (1.1)³

⇒ 15000 × 1.331 = 19965

∴ The correct answer is Rs. 19,965.

Alternate Method

Given:

Principal (P) = Rs. 15000

Rate (R) = 10% per annum

Time (n) = 3 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 15000 × (1 + 10/100)³

⇒ A = 15000 × (11/10) × (11/10) × (11/10)

⇒ A = 15 × 11 × 11 × 11

⇒ A = 15 × 1331

⇒ A = 19965

∴ The correct answer is Rs. 19,965.

Additional Information

Effective Rate Method

For 10% interest for 3 years, the effective compound interest rate is 33.1%. CI = 33.1% of 15000 = 4965. Amount = 15000 + 4965 = 19965.

Difference between SI and CI

For 3 years, the difference between CI and SI is given by P(R/100)² × (3 + R/100).

Compound Interest Formula

CI = Amount − Principal = P[(1 + R/100)ⁿ − 1].

Shortcut Trick

Ratio of Circumferences (C₁ : C₂) = 3 : 5

Ratio of Radii (r₁ : r₂) = 3 : 5 (since C ∝ r)

Ratio of Areas (A₁ : A₂) = 3² : 5² = 9 : 25

Percentage increase = [(25 − 9) ÷ 9] × 100 = (16 ÷ 9) × 100 = 177.78%

∴ The correct answer is 177.78 %.

Alternate Method

Given: Ratio of Circumferences = 3 : 5

Formula Used: Circumference = 2πr; Area = πr²

⇒ 2πr₁ ÷ 2πr₂ = 3 ÷ 5

⇒ r₁ ÷ r₂ = 3 ÷ 5

⇒ Area₁ = π × (3x)² = 9πx²

⇒ Area₂ = π × (5x)² = 25πx²

⇒ Difference in Area = 25πx² − 9πx² = 16πx²

⇒ Percentage Greater = (16πx² ÷ 9πx²) × 100

⇒ Percentage Greater = (16 ÷ 9) × 100 ≈ 177.78%

∴ The correct answer is 177.78 %.

Additional Information

Ratio Relationships in Circles

If the ratio of radii or circumferences is a : b, then the ratio of their areas is always a² : b².

Percentage Change Formula

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100. In this case, "greater than" refers to the smaller circle as the base.

Common Fractional Conversions

The fraction 1/9 ≈ 11.11%, hence 16/9 = 1 + 7/9 = 100% + 77.77% = 177.78%.

Shortcut Trick

Total Capacity (LCM of 3, 5, 15) = 15 units.

Efficiencies: A = 5, B = 3, C = −1. Sequence: B, A, C.

Work in 1 cycle (3 hours): 3 + 5 − 1 = 7 units.

In 2 cycles (6 hours): 7 × 2 = 14 units. Remaining work = 15 − 14 = 1 unit.

Next is B: Time taken = 1/3 hour. Total time = 6 + 1/3 = 19/3 hours.

∴ The correct answer is 19/3 hours.

Alternate Method

Given: Pipe A fills in 3 hours, Pipe B fills in 5 hours, Pipe C empties in 15 hours. Working alternatively starting from B.

The sequence of work is B → A → C.

⇒ Work in Hour 1 (B) = 3 units

⇒ Work in Hour 2 (A) = 5 units

⇒ Work in Hour 3 (C) = −1 unit

⇒ Total work in 1 cycle (3 hours) = 3 + 5 − 1 = 7 units

⇒ Work in 2 cycles (6 hours) = 7 × 2 = 14 units

⇒ Remaining work = 15 − 14 = 1 unit

⇒ Remaining work will be done by Pipe B in 1/3 hour.

⇒ Total time = 6 + 1/3 = 19/3 hours

∴ The correct answer is 19/3 hours.

Additional Information

Alternate Work Concept

When pipes work alternatively, calculate the work done in one complete cycle before repeating the process for the total capacity.

Negative Efficiency

For an outlet or emptying pipe, the efficiency is always taken as negative in the total work calculation.

Pipes and Cisterns Formula

Total Work = Time × Efficiency. If multiple pipes work together, add their efficiencies: (E₁ + E₂ − E₃) × T = Total Work.

Shortcut Trick

Present ratio Munna : Guddu = 2 : 1 (Difference = 1 unit)

Ratio after 8 years = 6 : 5 (Difference = 1 unit)

Difference in Munna's age parts = 6 − 2 = 4 units

4 units → 8 years ⇒ 1 unit → 2 years

Munna's present age = 2 × 2 = 4 years

Munna's age after 6 years = 4 + 6 = 10 years

∴ The correct answer is 10 years.

Alternate Method

Given:

Present age of Guddu = x

Present age of Munna = 2x

Formula Used: Ratio = (Munna's Age + 8) / (Guddu's Age + 8)

Calculations:

⇒ (2x + 8) / (x + 8) = 6 / 5

⇒ 5 × (2x + 8) = 6 × (x + 8)

⇒ 10x + 40 = 6x + 48

⇒ 10x − 6x = 48 − 40

⇒ 4x = 8

⇒ x = 2

⇒ Munna's present age = 2 × 2 = 4 years

⇒ Munna's age after 6 years = 4 + 6 = 10 years

∴ The correct answer is 10 years.

Additional Information

Ratio Adjustment Method

If the difference between ratio parts is not the same, multiply the ratios by the difference of the other ratio to equalize the age gap.

Age Problems Tip

The difference between the ages of two people always remains constant regardless of the number of years passed.

General Solution:

Number of movie tickets sold in app A = 350

Number of movie tickets sold in app B = 350 + 10 = 360

Number of IPL tickets sold in app A = 7x

Number of IPL tickets sold in app B = 8x

Number of IPL tickets sold in app C = (8x - 230)

Total movie and IPL tickets sold in app C = 275 ×  2 = 550

Number of movie tickets sold in app C = 550/11 ×  6 = 300

Number of IPL tickets sold in app C = (550 - 300) = 250

To find the value of x 

(8x - 230) = 250

8x = 480

x = 60

Number of IPL tickets sold in app A = 420

Number of IPL tickets sold in app B = 480

 

 

Solution:

Number of movie tickets sold in app B = 360

Number of movie tickets sold in app C = 300

Number of IPL tickets sold in app A = 420

Number of IPL tickets sold in app B = 480

Required ratio = (360 + 300): (420 + 480) = 660: 900 

= 11: 15

General Solution:

Number of movie tickets sold in app A = 350

Number of movie tickets sold in app B = 350 + 10 = 360

Number of IPL tickets sold in app A = 7x

Number of IPL tickets sold in app B = 8x

Number of IPL tickets sold in app C = (8x - 230)

Total movie and IPL tickets sold in app C = 275 ×  2 = 550

Number of movie tickets sold in app C = 550/11 ×  6 = 300

Number of IPL tickets sold in app C = (550 - 300) = 250

To find the value of x 

(8x - 230) = 250

8x = 480

x = 60

Number of IPL tickets sold in app A = 420

Number of IPL tickets sold in app B = 480

 

Solution:

Number of movie tickets sold to males in app A = 350 ×  3/7 = 150

Number of movie tickets sold to females in app A = (350 - 150) = 200

Number of IPL tickets sold to females in app A = 420/6 = 70

Number of IPL tickets sold to males in app A = (420 - 70) = 350

Required sum = (150 + 350) = 500

General Solution:

Number of movie tickets sold in app A = 350

Number of movie tickets sold in app B = 350 + 10 = 360

Number of IPL tickets sold in app A = 7x

Number of IPL tickets sold in app B = 8x

Number of IPL tickets sold in app C = (8x - 230)

Total movie and IPL tickets sold in app C = 275 ×  2 = 550

Number of movie tickets sold in app C = 550/11 ×  6 = 300

Number of IPL tickets sold in app C = (550 - 300) = 250

To find the value of x 

(8x - 230) = 250

8x = 480

x = 60

Number of IPL tickets sold in app A = 420

Number of IPL tickets sold in app B = 480

 

 

Solution:

1/5^th of the movie tickets sold in app A = 350/5 = 70

1/6^th of the IPL tickets sold in app B = 480/6 = 80

Required sum = (80 + 70) = 150

Given Series:

(?), 3125, 256, 27, 4, 1

The logic followed here is as follows:

⇒ (6)⁶ = 46656

⇒ (5)⁵ = 3125

⇒ (4)⁴ = 256

⇒ (3)³ = 27

⇒ (2)² = 4

⇒ (1)¹ = 1

Hence, 46656 will come in the place of (?).

Given Series:

43, 50, 39, 52, 35, (?)

The logic followed here is as follows:

⇒ 43 + 7 = 50

⇒ 50 - 11 = 39

⇒ 39 + 13 = 52

⇒ 52 - 17 = 35

⇒ 35 + 19 = 54

Hence, 54 will come in the place of (?).

Given Series:

51, 100, 151, 205, 264, (?)

The logic followed here is as follows:

⇒ 51 + 49 = 100

⇒ 100 + 51 = 151

⇒ 151 + 54 = 205

⇒ 205 + 59 = 264

⇒ 264 + 66 = 330

Hence, 330 will come in the place of (?).

Given Series:

120, 139, 167, 213, 295, (?)

The logic followed here is as follows:

⇒ 111 + 9 = 120

⇒ 121 + 18 = 139

⇒ 131 + 36 = 167

⇒ 141 + 72 = 213

⇒ 151 + 144 = 295

⇒ 161 + 288 = 449

Hence, 449 will come in the place of (?).

The series follows the following pattern:

13 + 1 = 2

23 + 2 = 10

33 + 3 = 30

43 + 4 = 68

53 + 5 = 130

63 + 6 = 222

∴ The missing term in the series is 130.

Shortcut Trick

Successive remaining percentage method: 20% = 1/5, so remaining part = 4/5.

Let initial amount be X. Total remaining fraction = 4/5 × 4/5 = 16/25.

Given: 16 units = 12800 → 1 unit = 800.

Initial amount (25 units) = 25 × 800 = 20,000.

∴ The correct answer is Rs. 20,000.

Alternate Method

Given: Percentage given to wife = 20%; Percentage of remaining given to charity = 20%; Final balance = Rs. 12800.

Formula: Final Amount = Initial Amount × (1 − r₁/100) × (1 − r₂/100)

⇒ Let initial amount be X.

⇒ Amount after giving to wife = X × (100 − 20)/100 = 0.80X

⇒ Amount after charity = 0.80X × (100 − 20)/100 = 0.80X × 0.80 = 0.64X

⇒ 0.64X = 12800

⇒ X = 12800 ÷ 0.64

⇒ X = 1280000 ÷ 64 = 20000

∴ The correct answer is Rs. 20,000.

Additional Information

Successive Percentage Change

When values change on the remaining balance, the net change is calculated as a + b + (ab/100). For reductions, use negative values.

Base Value Concept

Always identify the base for each percentage. In remaining value problems, the base changes after every step.

Fractional Equivalent

Using fractions like 20% = 1/5 makes calculations faster: (Initial) × (4/5) × (4/5) = Final.

Shortcut Trick

Initial Ratio (Milk : Water) = 7 : 8

Final Ratio (Water : Milk) = 3 : 2 → (Milk : Water) = 2 : 3

Using Cross-Multiplication Method: (7 × 3 − 8 × 2) units = (10 × 2 − 5 × 3) litres

(21 − 16) units = (20 − 15) litres ⇒ 5 units = 5 litres ⇒ 1 unit = 1 litre

Initial total quantity = (7 + 8) units = 15 units = 15 × 1 = 15 litres.

∴ The correct answer is 15 litres.

Alternate Method

Given: Initial Ratio M:W = 7:8. Let initial milk = 7x and initial water = 8x.

Formula: (Milk + added Milk) / (Water + added Water) = Final Milk / Final Water

⇒ Final Water : Milk = 3 : 2 ⇒ Final Milk : Water = 2 : 3

⇒ (7x + 5) / (8x + 10) = 2 / 3

⇒ 3 × (7x + 5) = 2 × (8x + 10)

⇒ 21x + 15 = 16x + 20

⇒ 21x − 16x = 20 − 15

⇒ 5x = 5 ⇒ x = 1

⇒ Initial quantity = 7x + 8x = 15x

⇒ Initial quantity = 15 × 1 = 15 litres

∴ The correct answer is 15 litres.

Additional Information

Ratio and Proportion Basics

A ratio a:b indicates the relative size of two quantities. The total quantity is the sum of the ratio parts multiplied by a common constant x.

Alligation Method

Used to find the mean value of a mixture when two ingredients of different prices or concentrations are mixed together.

Mixture Replacement Formula

Final Quantity = Initial Quantity × (1 − y/x)ⁿ, where y is the amount replaced and x is the total volume.

Solution:

Number of questions attempted by person P in subject C = 56

Number of questions attempted by person Q in subject C = 42

Number of questions attempted by person R in subject A = 58

Required percentage = (56 + 42)/58 ×  100 = 168.96% ~ 169%

Solution:

Total questions attempted by person Q from subjects  A to F = 60 ×  6 = 360

Total questions attempted by person R from subjects A to F = 70 ×  6 = 420

Number of questions attempted by person Q in subject F = 360 - (80 + 52 + 42 + 76 + 64) = 46

Number of questions attempted by person R in subject F = 420 - (58 + 66 + 38 + 62 + 78) = 118

Required difference = (118 - 46) = 72

Solution:

Number of questions attempted by person P in subject B = 48

Number of questions attempted by person Q in subject B = 52

Number of questions attempted by person P in subject E = 72

Number of questions attempted by person R in subject E = 78

Required ratio = (100 : 150) = 2: 3

Solution:

Number of questions attempted by person P in subject B = 48

Number of questions attempted by person S in subject B = 48 ×  125/100 = 60

Number of questions attempted by person Q in subject B = 52

Number of questions attempted by person T in subject B = 52 ×  150/100 = 78

Required sum = (60 + 78) = 138

Solution:

Total marks scored by person Q = 234

Total questions attempted = (80 + 52 + 42 + 76 + 64) = 314

Number of wrong questions = x

(314 - x) ×  1 - (x × 1/4) = 234

(314  - x) -  0.25x = 234

x = 80/1.25

x = 64

∴ Number of wrong questions attempted by Person Q is 64.