Quantitative Aptitude PYQs

We are given:

Total mobile covers sold by C in March = 88.

The ratio of blue color mobile covers to black color mobile covers sold by C in March is 4:7.

Let the number of blue color mobile covers be 4x, and the number of black color mobile covers be 7x.

4x + 7x = 88

11x = 88

x = 88 / 11 = 8

Black color mobile covers = 7x = 7 × 8 = 56

Thus, the number of black color mobile covers sold by C in March is 56.

A's sales in March = 94

B's sales in March = 120

Total =94 + 120 = 214 

C's sales in May = 70

C's sales in March = 88

Total =70 + 88 = 158 

The ratio of the number of mobile covers sold by A and B together in March to the number of mobile covers sold by C in May and March together is:

Ratio = A and B in March / C in May and March = 214 / 158

Simplify the ratio by dividing both numbers by 2:

214 / 158 = 107 / 79

Thus, the ratio is 107:79.

Shortcut Trick

Breadth 3 units = 12 cm → 1 unit = 4 cm.

Length = 5 × 4 = 20 cm.

Side of Square = (Length + Breadth) ÷ 2 = (20 + 12) ÷ 2 = 16 cm.

Radius of Circle = Side of Square = 16 cm.

Area of Circle = π × (16)² = 256π cm².

∴ The correct answer is 256π cm².

Alternate Method

Given: Ratio L:B = 5:3, Breadth = 12 cm, Perimeter_rect = Perimeter_sq, Side_sq = Radius_circle.

Formula Used: Perimeter of rectangle = 2(L + B); Perimeter of square = 4 × Side; Area of circle = πr².

⇒ 3 units = 12 cm

⇒ 1 unit = 4 cm

⇒ Length = 5 × 4 = 20 cm

⇒ Perimeter of rectangle = 2(20 + 12) = 64 cm

⇒ Perimeter of square = 64 cm

⇒ 4 × Side = 64 ⇒ Side = 16 cm

⇒ Radius (r) = 16 cm

⇒ Area of circle = π × (16)² = 256π cm²

∴ The correct answer is 256π cm².

Additional Information

Rectangle Properties

Perimeter = 2(l + b) and Area = l × b. Diagonal d = √(l² + b²).

Square Properties

Perimeter = 4a and Area = a². Diagonal d = a√2.

Circle Properties

Circumference = 2πr and Area = πr². Diameter D = 2r.

Shortcut Trick

Given ratio a : d = 3 : 8 and d = 16.

⇒ a = (3/8) × 16 = 6.

Given a : b = 3 : 5. Since a = 6 (which is 2 × 3), then b = 2 × 5 = 10.

Checking consistency: Since b/c = c/d, then c² = b × d = 10 × 16 = 160, which is valid for positive numbers.

∴ The correct answer is 10.

Alternate Method

Given: a : b = 3 : 5, b/c = c/d, a : d = 3 : 8, and d = 16.

⇒ From ratio a : d = 3 : 8 and d = 16:

⇒ a/16 = 3/8

⇒ a = (3 × 16) ÷ 8 = 6

⇒ Now using ratio a : b = 3 : 5:

⇒ 6/b = 3/5

⇒ 3 × b = 6 × 5

⇒ 3b = 30

⇒ b = 10

∴ The correct answer is 10.

Additional Information

Continued Proportion

When a, b, c are in continued proportion, then a/b = b/c, which implies b² = ac. Here b is the mean proportional.

Ratio Scaling

If a : b = m : n, and the value of a is known, then b = (a × n) ÷ m.

Compound Ratio

The compound ratio of a : b and c : d is (a × c) : (b × d).

Shortcut Trick

Let total students = 4 and class average = 100.

Total score = 4 × 100 = 400.

Score of 3 students = 3 × 80% of 100 = 3 × 80 = 240.

Score of remaining 1 student = 400 − 240 = 160.

Ratio = 160 : 100 = 8 : 5.

∴ The correct answer is 8 : 5.

Alternate Method

Given:

⇒ Let total number of students = n

⇒ Let Entire Class Average = A

⇒ Total Score = n × A

Calculations:

⇒ Number of students in 3/4^th group = (3/4)n

⇒ Average of this group = 80% of A = 0.8A

⇒ Total score of this group = (3/4)n × 0.8A = 0.6nA

⇒ Remaining students = n − (3/4)n = (1/4)n

⇒ Total score of remaining students = nA − 0.6nA = 0.4nA

⇒ Average of remaining students = 0.4nA ÷ (1/4)n = 0.4A × 4 = 1.6A

⇒ Required Ratio = 1.6A : A = 1.6 : 1 = 16 : 10

⇒ Simplified Ratio = 8 : 5

∴ The correct answer is 8 : 5.

Additional Information

Weighted Average Formula

Total Average (A_v) = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂), where n is the quantity and a is the average.

Deviation Method

The sum of deviations of individual groups from the total average must be zero: n₁(a₁ − A_v) + n₂(a₂ − A_v) = 0.

Shortcut Trick

Net change percentage = a + b + (a × b) ÷ 100

Here, a = −20% (loss) and b = +40% (profit).

Net profit% = −20 + 40 + (−20 × 40) ÷ 100 = 20 − 8 = 12%.

Overall profit = 12% of 6000 = 0.12 × 6000 = 720.

∴ The correct answer is 720 Rs.

Alternate Method

Given → Initial Cost Price (CP₁) = 6000 Rs, Loss% = 20%, Profit% on second item = 40%. Formulas: SP = CP × (100 ± Gain/Loss)% ÷ 100 | Overall Profit = Final SP − Initial CP.

⇒ Selling Price of first product (SP₁) = 6000 × (100 − 20) ÷ 100 = 6000 × 0.8 = 4800 Rs.

⇒ Cost Price of second product (CP₂) = SP₁ = 4800 Rs.

⇒ Selling Price of second product (SP₂) = 4800 × (100 + 40) ÷ 100 = 4800 × 1.4 = 6720 Rs.

⇒ Overall Profit = Final SP − Initial CP = 6720 − 6000 = 720 Rs.

∴ The correct answer is 720 Rs.

Additional Information

Successive Percentage Change

When a value is changed by x% and then the resulting value is changed by y%, the net change is (x + y + xy/100)%.

Profit and Loss Basics

Profit occurs when SP > CP. Loss occurs when CP > SP. Both are always calculated on the CP unless stated otherwise.

Shortcut Trick

Ratio of Profit of B to Total = 3 : 11, so ratio of Profit A : B = (11 − 3) : 3 = 8 : 3.

Ratio of Investments × Time = Profit Ratio.

(2400 × 12) ÷ (x × 4) = 8 ÷ 3.

(600 × 12) ÷ x = 8 ÷ 3 ⇒ 7200 ÷ x = 8 ÷ 3.

x = (7200 × 3) ÷ 8 = 900 × 3 = 2700.

∴ The correct answer is ₹2700.

Alternate Method

Given → Investment of A = ₹2400, Time of A = 12 months, Time of B = 12 − 8 = 4 months. Profit of B = 3/11 of Total. Formulas: Profit Ratio = (Investment_A × Time_A) : (Investment_B × Time_B).

⇒ Total Profit = 11 units, B Profit = 3 units, A Profit = 11 − 3 = 8 units. ⇒ (2400 × 12) ÷ (x × 4) = 8 ÷ 3 ⇒ 28800 ÷ 4x = 8 ÷ 3 ⇒ 7200 ÷ x = 8 ÷ 3 ⇒ 8x = 21600 ⇒ x = 2700.

∴ The correct answer is ₹2700.

Additional Information

Partnership Concept

When multiple persons invest capital for different time periods, the profit is distributed in the ratio of the product of their capital and time.

Investment Formula

Investment = Profit ÷ Time. If the profit ratio and time ratio are known, the investment ratio can be calculated directly.

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

 

Calculations:

The formula to calculate the percentage is:

Percentage = (Part / Whole) × 100

Here:

Part = Fine Arts in T = 54

Whole = Total Arts in T = 120

Substitute the values into the formula:

Percentage = (54 / 120) × 100 = 45%.

Thus, the correct answer is 45%

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

 

Calculations:

From the table:

Total Arts in T = 120

We need to check the sum of Visual Arts for each pair of exhibitions and see which one equals 120.

Pair 1: S and T

Visual Arts in S = 60

Visual Arts in T = 66

Total = 60 + 66 = 126

126 ≠ 120 → Not a match.

Pair 2: P and R

Visual Arts in P = 45

Visual Arts in R = 65

Total = 45 + 65 = 110

110 ≠ 120 → Not a match.

Pair 3: Q and T

Visual Arts in Q = 54

Visual Arts in T = 66

Total = 54 + 66 = 120

120 = 120 → Match!

Pair 4: Q and R

Visual Arts in Q = 54

Visual Arts in R = 65

Total = 54 + 65 = 119

119 ≠ 120 → Not a match.

Pair 5: P and S

Visual Arts in P = 45

Visual Arts in S = 60

Total = 45 + 60 = 105

105 ≠ 120 → Not a match.

The pair Q and T has a sum of Visual Arts equal to the Total Arts in Exhibition T.

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

 

Calculations:

From the table:

Fine Arts in R and T together:

Fine Arts in R = 60

Fine Arts in T = 54

Total Fine Arts in R and T = 60 + 54 = 114

Total Arts in P = 114

The ratio of the number of Fine Arts in R and T together to the number of Total Arts in P is:

Ratio = Fine Arts in R and T / Total Arts in P = 114 / 1 = 1:1

Thus, the correct answer is 1:1.

General Solution:

The given data represents the Total Arts and Visual Arts across 5 exhibitions (P, Q, R, S, T). From this, we can derive the Fine Arts for each exhibition using the formula:

Fine Arts = Total Arts − Visual Arts

Using the formula above, we calculate the Fine Arts for each exhibition:

Exhibition P:

Fine Arts = 114 − 45 = 69

Exhibition Q:

Fine Arts = 108 − 54 = 54

Exhibition R:

Fine Arts = 125 − 65 = 60

Exhibition S:

Fine Arts = 96 − 60 = 36

Exhibition T:

Fine Arts = 120 − 66 = 54

Thus,

 

Calculations:

From the table, we know the Fine Arts for each exhibition:

Exhibition P: Fine Arts = 69

Exhibition R: Fine Arts = 60

To find the total number of Fine Arts in P and R together, we add the Fine Arts of P and R:

Total Fine Arts (P + R) = 69 + 60 = 129

Thus, the total number of Fine Arts in P and R together is 129.

Shortcut Trick

Let total workers be 100%.

Workers above 45 years = 50%.

Female workers above 45 = 60% of 50% = 30%.

Given, 30% = 1200 ⇒ 1% = 40.

Total workers = 100% = 100 × 40 = 4000.

∴ The correct answer is 4000 workers.

Alternate Method

Given: Female workers above 45 = 1200; % Above 45 = 50%; % Female in that group = 60%.

Formula: Total Workers × % Above 45 × % Female = 1200

⇒ Let Total workers be x.

⇒ x × (50/100) × (60/100) = 1200

⇒ x × (1/2) × (3/5) = 1200

⇒ x × (3/10) = 1200

⇒ x = (1200 × 10) ÷ 3

⇒ x = 400 × 10 = 4000

∴ The correct answer is 4000 workers.

Additional Information

Successive Percentage Change

When percentages are applied sequentially on a base value, the effective percentage is P₁ × P₂ / 100.

Base Value Concept

Always identify the base (100%) correctly; in this case, females are 60% of the 50% subset, not the whole population.

Shortcut Trick

Overall interest rate per annum = (6720 ÷ 4) × 100 ÷ 12000 = 14%.

Using Alligation: (Scheme 1: 10%) vs (Scheme 2: 20%) with Mean (14%).

Ratio of investments = (20 − 14) : (14 − 10) = 6 : 4 = 3 : 2.

Amount @ 20% = (2 ÷ 5) × 12000 = 4800.

∴ The correct answer is Rs. 4800.

Alternate Method

Given: Total Principal (P) = Rs. 12000, Total SI = Rs. 6720, Time (T) = 4 years, R₁ = 10%, R₂ = 20%.

Formula: SI = (P × R × T) ÷ 100

⇒ Let the amount lent at 20% be Rs. x.

⇒ Amount lent at 10% = (12000 − x).

⇒ [(12000 − x) × 10 × 4] ÷ 100 + [x × 20 × 4] ÷ 100 = 6720

⇒ (12000 − x) × 40 + 80x = 672000

⇒ 480000 − 40x + 80x = 672000

⇒ 40x = 672000 − 480000

⇒ 40x = 192000

⇒ x = 192000 ÷ 40 = 4800

∴ The correct answer is Rs. 4800.

Additional Information

Simple Interest (SI)

The interest remains constant every year on the original principal. SI = (P × R × T) ÷ 100.

Alligation in Interest

When a sum is divided into two parts with different rates, the ratio of parts = (Rate₂ − Avg Rate) : (Avg Rate − Rate₁).

Effective Annual Rate

If interest is calculated for multiple years, the total percentage interest is R × T%.

Shortcut Trick

Ratio of Mohan's age to (Mohan + Krishna) = 40% = 2 : 5.

If Mohan = 2 units and Sum = 5 units, then Krishna = 5 − 2 = 3 units.

Difference = 3 − 2 = 1 unit → 12 years.

Mohan's current age = 2 × 12 = 24 years.

Mohan's age after 8 years = 24 + 8 = 32 years.

∴ The correct answer is 32 years.

Alternate Method

Given: Krishna = Mohan + 12

Formula: Mohan = 0.40 × (Mohan + Krishna)

⇒ M = 0.4(M + M + 12)

⇒ M = 0.4(2M + 12)

⇒ M = 0.8M + 4.8

⇒ 0.2M = 4.8

⇒ M = 4.8 ÷ 0.2 = 24 years

⇒ Age after 8 years = 24 + 8 = 32 years

∴ The correct answer is 32 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant throughout their lives, regardless of the number of years passed.

Percentage to Ratio Conversion

Always convert percentages to simple fractions (e.g., 40% = 2/5) to solve ratio-based age problems faster without using variables.

Shortcut Trick

Let breadth = x and length = 4x.

New Area − Old Area = 880

(4x + 20)(x + 30) − 4x² = 880

120x + 20x + 600 = 880 ⇒ 140x = 280 ⇒ x = 2 cm.

Length = 4 × 2 = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given: Length (L) = 4 × Breadth (B); L_new = L + 20; B_new = B + 30; Area Increase = 880 cm².

Formula: Area of Rectangle = Length × Breadth

⇒ Original Area = 4x × x = 4x²

⇒ New Area = (4x + 20)(x + 30) = 4x² + 120x + 20x + 600

⇒ (4x² + 140x + 600) − 4x² = 880

⇒ 140x + 600 = 880

⇒ 140x = 280

⇒ x = 2 cm

⇒ Length = 4x = 4 × 2 = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Perimeter of Rectangle

The total boundary length of a rectangle is given by 2 × (Length + Breadth).

Diagonal of Rectangle

The distance between opposite corners is calculated using Pythagoras theorem: d = √(L² + B²).

Area Change Percentage

If length increases by a% and breadth by b%, net area change % = a + b + (a × b)/100.

Concept used:

We have to follow the BODMAS rule

Calculation:

√4 × 100% of 26 = 13 × ?

⇒ 2 × 1 of 26 = 13 × ?

⇒ 2 × 26 = 13 × ?

⇒ 52/13 = ?

⇒ ? = 4

∴ The value of ? is 4

Concept:

We have to follow the BODMAS rule

Calculation:

50% of 250 + 125 = ? – 50

⇒ 125 + 125 + 50 = ?

⇒ 250 + 50 = ?

⇒ 300 = ?

∴ 300 will come in place of question mark.

Calculation:

24% of 120 + 35% of 560 = ?

⇒ 28.8 + 196 = ?

⇒ 224.8 = ?

∴ 224.8 will come in place of the question mark

Concept:

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

Calulation:

√1296 - √576 = √? + 3 × 2

⇒ 36 – 24 = √? + 6

⇒ 12 = √? + 6

⇒ √? = 6

⇒ ? = 36

∴ The value of ? is 36

Concept used:

Calculation:

{(219 + 24) × 3}^1/2 = ?/5

⇒ {243 × 3}^1/2 = ?/5

⇒ {729}^1/2 = ?/5

⇒ 27 = ?/5

⇒ ? = 135

∴ The value of ? is 135.