Quantitative Aptitude PYQs

Number of students in commerce department is 70 more than the number of students in 2017.

So, 30%  - 20% = 70

Or, 10% = 70

Or, 100% = 700

So, total number of students in commerce department is 700.

Number of students in commerce department in 2017  is  700 × 20/100 = 140

Number of students in science department in 2017 is 140 – 40 = 100

So, number of student in 2017 in two department together is 140 + 100 = 240.

Total value of pie chart is 100%

So, 12% + x% + 30% + 25% + [x-3]% = 100

Or, 2x = 100 – 12 – 30 -25 +3 = 36

Or, x = 36 /2 = 18

So, Percentage of students in science and commerce department together in 2017 is 18 – 3 = 15%

So, 15% = 240

Or, 100% = [ 240/15] ×100 =1600

 

Calculation

Number of female students in 2016 science department is 190 × 2/5 = 76

So, 4m = 76, m = 76 / 4 = 19

Number of students in commerce department is 70 more than the number of students in 2017.

So, 30%  - 20% = 70

Or, 10% = 70

Or, 100% = 700

So, total number of students in commerce department is 700.

Number of students in commerce department in 2017  is  700 × 20/100 = 140

Number of students in science department in 2017 is 140 – 40 = 100

So, number of student in 2017 in two department together is 140 + 100 = 240.

Total value of pie chart is 100%

So, 12% + x% + 30% + 25% + [x-3]% = 100

Or, 2x = 100 – 12 – 30 -25 +3 = 36

Or, x = 36 /2 = 18

So, Percentage of students in science and commerce department together in 2017 is 18 – 3 = 15%

So, 15% = 240

Or, 100% = [ 240/15] ×100 =1600

 

Calculation

Number of students in arts department in 2014 is 5x + 20 = 5 ×18 + 20 = 110

So, required difference is 204 – 110 = 94

Number of students in commerce department is 70 more than the number of students in 2017.

So, 30%  - 20% = 70

Or, 10% = 70

Or, 100% = 700

So, total number of students in commerce department is 700.

Number of students in commerce department in 2017  is  700 × 20/100 = 140

Number of students in science department in 2017 is 140 – 40 = 100

So, number of student in 2017 in two department together is 140 + 100 = 240.

Total value of pie chart is 100%

So, 12% + x% + 30% + 25% + [x-3]% = 100

Or, 2x = 100 – 12 – 30 -25 +3 = 36

Or, x = 36 /2 = 18

So, Percentage of students in science and commerce department together in 2017 is 18 – 3 = 15%

So, 15% = 240

Or, 100% = [ 240/15] ×100 =1600

 

Calculation

Number of students in science department is 190

Number of students in commerce department is 210.

So, required ratio = 190 : 210 = 19:21 = m : n

So, m = 19, n = 21

So, 3m + 4n =3×19 + 4 ×21 = 141

Number of students in commerce department is 70 more than the number of students in 2017.

So, 30%  - 20% = 70

Or, 10% = 70

Or, 100% = 700

So, total number of students in commerce department is 700.

Number of students in commerce department in 2017  is  700 × 20/100 = 140

Number of students in science department in 2017 is 140 – 40 = 100

So, number of student in 2017 in two department together is 140 + 100 = 240.

Total value of pie chart is 100%

So, 12% + x% + 30% + 25% + [x-3]% = 100

Or, 2x = 100 – 12 – 30 -25 +3 = 36

Or, x = 36 /2 = 18

So, Percentage of students in science and commerce department together in 2017 is 18 – 3 = 15%

So, 15% = 240

Or, 100% = [ 240/15] ×100 =1600

 

Calculation

Total number of students in science department in 2014 and 2015 is 204 + 340 = 544

Total number of students in commerce department in 2014 and 2015 is

84 + 140 = 224

So, required difference 544 – 224 = 320

Number of students in commerce department is 70 more than the number of students in 2017.

So, 30%  - 20% = 70

Or, 10% = 70

Or, 100% = 700

So, total number of students in commerce department is 700.

Number of students in commerce department in 2017  is  700 × 20/100 = 140

Number of students in science department in 2017 is 140 – 40 = 100

So, number of student in 2017 in two department together is 140 + 100 = 240.

Total value of pie chart is 100%

So, 12% + x% + 30% + 25% + [x-3]% = 100

Or, 2x = 100 – 12 – 30 -25 +3 = 36

Or, x = 36 /2 = 18

So, Percentage of students in science and commerce department together in 2017 is 18 – 3 = 15%

So, 15% = 240

Or, 100% = [ 240/15] ×100 =1600

 

Calculation

Total number of students in science department in five year is 1600 – 700 = 900

So, average is 900 / 5 = 180

So, Number of students in science department in 2018  is 180 + 25 = 205

Shortcut Trick

Let initial quantity be 15x and final be 11x.

Change in quantity: 15x − 28 + 16 = 11x ⇒ 4x = 12 ⇒ x = 3.

Initial mixture = 15 × 3 = 45 liters. Final mixture = 11 × 3 = 33 liters.

Final Water = Final Mixture − Final Milk = 33 − 26.2 = 6.8 liters.

Since 16L milk was added, water quantity remains same after taking out 28L: Water in (45−28)L = 6.8L.

Initial water % = (6.8 / 17) × 100 = 40%.

∴ The correct answer is 40%.

Alternate Method

Given: Initial/Final ratio = 15:11, Removal = 28L, Addition (Milk) = 16L, Final Milk = 26.2L.

⇒ Let initial quantity = 15x and final quantity = 11x.

⇒ 15x − 28 + 16 = 11x

⇒ 4x = 12 ⇒ x = 3

⇒ Total initial quantity = 45 liters; Total final quantity = 33 liters.

⇒ Water in final mixture = 33 − 26.2 = 6.8 liters.

⇒ Since only milk was added, water in (45 − 28) = 17 liters of mixture is 6.8 liters.

⇒ Initial water ratio = 6.8 / 17 = 0.4

⇒ Initial water percentage = 0.4 × 100 = 40%

∴ The correct answer is 40%.

Additional Information

Mixture Removal Property

When a part of a mixture is removed, the ratio of ingredients in the remaining mixture and the removed portion remains the same as the initial ratio.

Replacement with Single Liquid

If only one component (e.g., milk) is added back, the quantity of the other component (water) in the mixture remains constant between the removal step and the final step.

Percentage Composition

Percentage of a component = (Quantity of component ÷ Total quantity of mixture) × 100.

Shortcut Trick

Ratio of CSA: πrl / 4πR² = 7 / 100

Given Slant height (l) = Radius of sphere (R) and r = 14 m.

Substituting: 14 × R / (4 × R²) = 7 / 100 ⇒ 14 / (4R) = 7 / 100 ⇒ 1 / (2R) = 1 / 100 ⇒ R = 50 m.

So, l = 50 m. Since r = 14 m, height (h) = √(50² − 14²) = 48 m.

Difference = 48 − 14 = 34 m.

∴ The correct answer is 34 m.

Alternate Method

Given: Radius of cone (r) = 14 m, Slant height (l) = Radius of sphere (R).

Formula Used: CSA of cone = πrl; CSA of sphere = 4πR²; l² = h² + r²

⇒ π × 14 × l = (7 / 100) × 4 × π × R²

⇒ 14 × l = (7 / 100) × 4 × l² (Since l = R)

⇒ 14 = (28 / 100) × l

⇒ l = (14 × 100) ÷ 28

⇒ l = 50 m

⇒ h² = l² − r² = 50² − 14²

⇒ h² = 2500 − 196 = 2304

⇒ h = √2304 = 48 m

⇒ Difference = h − r = 48 − 14 = 34 m

∴ The correct answer is 34 m.

Additional Information

Volume of Cone and Sphere

Volume of cone = (1/3)πr²h and Volume of sphere = (4/3)πR³.

Pythagorean Triplets

Common triplets like (7, 24, 25) can be scaled by 2 to get (14, 48, 50) for quick cone calculations.

Total Surface Area (TSA)

TSA of Cone = πr(l + r). Sphere TSA is same as its CSA = 4πR².

Shortcut Trick
Given Difference R − P = 4 and Product P × R = P2 + 56.
Substitute R = P + 4 ⇒ P(P + 4) = P2 + 56 ⇒ 4P = 56 ⇒ P = 14.
Then R = 18. Ratio P : (Q + R) = 2 : 5 ⇒ 14 : (Q + 18) = 2 : 5.
7 × 5 = Q + 18 ⇒ 35 = Q + 18 ⇒ Q = 17. Product P × Q = 14 × 17 = 238.
∴ The correct answer is 238.
Alternate Method

Given: P < Q < R, R − P = 4, PR = P2 + 56, P : (Q + R) = 2 : 5
⇒ PR − P2 = 56
⇒ P(R − P) = 56
⇒ P × 4 = 56
⇒ P = 14
⇒ R = 14 + 4 = 18
⇒ P / (Q + R) = 2 / 5
⇒ 14 / (Q + 18) = 2 / 5
⇒ 7 / (Q + 18) = 1 / 5
⇒ Q + 18 = 35
⇒ Q = 17
⇒ Product P × Q = 14 × 17 = 238
∴ The correct answer is 238.
Additional Information
Ratio and Proportion Properties
If a : b = c : d, then product of extremes equals product of means (a × d = b × c).
Algebraic Identities
Difference of squares: a2 − b2 = (a − b)(a + b). Factoring common terms often simplifies product equations.
Linear Equations
System of equations with 3 variables requires 3 independent conditions for a unique solution.

For shop A,

Let number of volleyball and football sold in shop A is 3x and 7x respectively.

So, difference between number of volleyball and football sold is 40

So, 7x – 3x = 40

Or, 4x = 40

Or, x = 40 / 4 = 10

So, Number of volleyballs sold in shop A is 3 × 10 = 30

Number of footballs sold in shop A is 7 × 10 = 70

Number of basketballs sold in shop A is 140 – 70 – 30 = 40

Calculation

Number of red color volleyball sold in shop A is 30 × 60 /100 = 18

Number of red color volleyball sold in shop B is 42 -18 = 24

Number of white color volleyball sold in shop B is 60 – 24 = 36

For shop A,

Let number of volleyball and football sold in shop A is 3x and 7x respectively.

So, difference between number of volleyball and football sold is 40

So, 7x – 3x = 40

Or, 4x = 40

Or, x = 40 / 4 = 10

So, Number of volleyballs sold in shop A is 3 × 10 = 30

Number of footballs sold in shop A is 7 × 10 = 70

Number of basketballs sold in shop A is 140 – 70 – 30 = 40

 

Calculation

Number of volleyballs sold in shop E 40

Number of basket ball sold in shop E is 50

So, x = 50 - 40 = 10

So, total number of basketballs sold in shop D and E together is 40 + 50 = 90 = 9x

For shop A,

Let number of volleyball and football sold in shop A is 3x and 7x respectively.

So, difference between number of volleyball and football sold is 40

So, 7x – 3x = 40

Or, 4x = 40

Or, x = 40 / 4 = 10

So, Number of volleyballs sold in shop A is 3 × 10 = 30

Number of footballs sold in shop A is 7 × 10 = 70

Number of basketballs sold in shop A is 140 – 70 – 30 = 40

 

Calculation

 

Sum of football sold in shop A and B is 70 + 50 = 120

Sum of volleyball sold in shop B and C is 60 +50 = 110

So, m = 120  and n = 110

So, m + n = 120 + 110 = 230

For shop A,

Let number of volleyball and football sold in shop A is 3x and 7x respectively.

So, difference between number of volleyball and football sold is 40

So, 7x – 3x = 40

Or, 4x = 40

Or, x = 40 / 4 = 10

So, Number of volleyballs sold in shop A is 3 × 10 = 30

Number of footballs sold in shop A is 7 × 10 = 70

Number of basketballs sold in shop A is 140 – 70 – 30 = 40

 

Calculation:

Number of balls sold in shop F is 160 × [100 + 20] /100 = 192

Number of volleyball and basketball sold in shop F is 192 × 50/100 = 96

For shop A,

Let number of volleyball and football sold in shop A is 3x and 7x respectively.

So, difference between number of volleyball and football sold is 40

So, 7x – 3x = 40

Or, 4x = 40

Or, x = 40 / 4 = 10

So, Number of volleyballs sold in shop A is 3 × 10 = 30

Number of footballs sold in shop A is 7 × 10 = 70

Number of basketballs sold in shop A is 140 – 70 – 30 = 40

 

Calculation:

Number of bat sold in shop D is 120 × 3 /4 = 90

Number of bat sold in shop B is 50 × 3 /2 = 75

So, total number of bats sold in shop B and D together is 90 + 75 = 165

Concept used :

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ 79.96% of 200.20 + 50.10 x 3.11 = ? + 25.20% of 60.13

⇒ 80/100 x 200 + 50 x 3 = ? + 25/100 x 60

⇒ 160 + 150 = ? + 15

⇒ 310 = ? + 15

⇒ ? = 295

Hence, the correct answer is option 3.

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 following BODMAS rule 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 the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

38.98 ÷ 12.99 × 16.97 + 43.94 = ? + 99.99 ÷ 4.97 × 6.98

⇒ 39 ÷ 13 × 17 + 44 = ? + 100 ÷ 5 × 7

⇒ 3 × 17 + 44 = ? + 20 × 7

⇒ 51 + 44 = ? + 140

⇒ 95 = ? + 140

⇒ 95 - 140 = ?

⇒ ? = - 45

Hence, -45 will come in the place of (?).

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 following BODMAS rule 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 the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

49.99 + ? ÷ 15.01 + 230.05 + 14.98% of 599.99 = 340.08

⇒ 50 + ? ÷ 15 + 230 + 15% of 600 = 340

⇒ 50 + ? ÷ 15 + 230 + 90 = 340

⇒ ? ÷ 15 + 370 = 340

⇒ ? ÷ 15 = - 30

⇒ ? = - 30 x 15

⇒ ? = -450

Hence, -450 will come in the place of (?).

Shortcut Trick

Ratio of CI Amounts: [12000 × (1 + r)²] ÷ [10000 × (1 + r)³] = 12/11

1.2 ÷ (1 + r) = 12/11 ⇒ 1 + r = 1.1 ⇒ r = 10%

New SI Rate = 10% + 5% = 15%

SI Amount = 8000 + (8000 × 15% × 3) = 8000 + 3600 = 11600

∴ The correct answer is Rs. 11600.

Alternate Method

Given: P₁ = Rs. 12000, T₁ = 2 years, P₂ = Rs. 10000, T₂ = 3 years, Ratio of Amounts = 12:11, New P = Rs. 8000, New T = 3 years, New Rate = (x + 5)%.

Formula Used: Amount (CI) = P(1 + r/100)ⁿ; Amount (SI) = P + (P × r × t)/100

⇒ [12000(1 + x/100)²] / [10000(1 + x/100)³] = 12 / 11

⇒ [1.2] / [1 + x/100] = 12 / 11

⇒ 1 + x/100 = (1.2 × 11) / 12 = 1.1

⇒ x/100 = 0.1 ⇒ x = 10%

⇒ New Rate = 10 + 5 = 15%

⇒ SI = (8000 × 15 × 3) / 100 = 3600

⇒ Total Amount = 8000 + 3600 = 11600

∴ The correct answer is Rs. 11600.

Additional Information

CI Amount Formula

The amount in Compound Interest is given by A = P(1 + r/100)ⁿ, where n is the number of conversion periods.

SI Amount Formula

The amount in Simple Interest is A = P + SI = P(1 + rt/100), where interest is calculated only on the principal.

Successive Ratio in CI

The ratio of amounts for successive years (n and n+1) in CI is always (1 + r/100).

Shortcut Trick

Ratio of A : B is 4 : 5. After x years, it becomes 5 : 6. Difference in parts (5−4 = 1, 6−5 = 1) is same, so 1 unit = x.

Ratio of B : C is 5 : 3. Before y years, it was 3 :

1. Difference in parts (5−3 = 2, 3−1 = 2) is same, so 2 units = y.

Given y = x + 5 ⇒ 2 units = 1 unit + 5 ⇒ 1 unit = 5 years.

Sum of present ages (4 + 5 + 3) = 12 units = 12 × 5 = 60 years.

∴ The correct answer is 60 years.

Alternate Method

Given: Ratio of present ages A : B : C = 4 : 5 : 3. Let common factor be k.

Formula: Ratio = (Initial age ± change) / (Initial age ± change)

⇒ For A and B: (4k + x) / (5k + x) = 5 / 6

⇒ 24k + 6x = 25k + 5x ⇒ x = k

⇒ For B and C: (5k − y) / (3k − y) = 3 / 1

⇒ 5k − y = 9k − 3y ⇒ 2y = 4k ⇒ y = 2k

⇒ Given y = x + 5 ⇒ 2k = k + 5 ⇒ k = 5

⇒ Sum of present ages = 4k + 5k + 3k = 12k

⇒ Total Age = 12 × 5 = 60 years

∴ The correct answer is 60 years.

Additional Information

Ratio Difference Method

When the same quantity is added or subtracted from both terms of a ratio, the difference between the ratio terms must be made equal to maintain proportionality.

Age Problems Property

The difference between the ages of two people always remains constant, regardless of how many years pass or have passed.

Shortcut Trick

Time taken for the second half of the journey = 420 ÷ 140 = 3 hours.

Remaining time for the first half of the journey = 6.5 − 3 = 3.5 hours.

Speed p = 420 ÷ 3.5 = 120 km/hr.

Time taken to cover 600 km at 120 km/hr = 600 ÷ 120 = 5 hours.

∴ The correct answer is 5 hours.

Alternate Method

Given: First distance = 420 km, Speed = p km/hr; Second distance = 420 km, Speed = 140 km/hr; Total time = 6 hours 30 minutes = 6.5 hours.

Formula Used: Time = Distance ÷ Speed

⇒ Total Time = Time₁ + Time₂

⇒ 6.5 = (420 ÷ p) + (420 ÷ 140)

⇒ 6.5 = (420 ÷ p) + 3

⇒ 420 ÷ p = 3.5

⇒ p = 420 ÷ 3.5 = 120 km/hr

⇒ Time taken to cover 600 km at speed p = 600 ÷ 120 = 5 hours

∴ The correct answer is 5 hours.

Additional Information

Average Speed for Equal Distances

When a body travels equal distances at speeds x and y, the average speed is given by 2xy ÷ (x + y).

Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Shortcut Trick

Profit = 1.5001 × Discount ≈ 1.5 × 1920.25 ≈ 2880.57.

Profit% ≈ 29.85% ⇒ CP = Profit ÷ 0.2985 ≈ 2880.57 ÷ 0.2985 ≈ 9650.

SP = CP + Profit ≈ 9650 + 2880.57 ≈ 12530.57.

MP = SP + Discount ≈ 12530.57 + 1920.25 ≈ 14450.82.

Discount% = (Discount ÷ MP) × 100 ≈ (1920.25 ÷ 14450.82) × 100 ≈ 13.28%.

∴ The correct answer is 13%.

Alternate Method

Given → Discount (D) ≈ 1920.25, Profit% (P%) ≈ 29.85%, Profit (P) ≈ 1.5001 × D.
Formulas: P = SP − CP | P% = (P ÷ CP) × 100 | MP = SP + D | Discount% = (D ÷ MP) × 100.

⇒ Profit = 1920.25 + (50.01% of 1920.25) ≈ 1920.25 + 960.32 = 2880.57.
⇒ CP = (Profit ÷ Profit%) × 100 ≈ (2880.57 ÷ 29.85) × 100 ≈ 9650.15.
⇒ SP = CP + Profit ≈ 9650.15 + 2880.57 = 12530.72.
⇒ MP = SP + Discount ≈ 12530.72 + 1920.25 = 14450.97.
⇒ Discount% = (1920.25 ÷ 14450.97) × 100 ≈ 13.287%.

∴ The correct answer is 13%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). MP = SP + Discount.

Profit Calculation

Profit is always calculated on the Cost Price (CP) unless stated otherwise. SP = CP + Profit.