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

25% of 480 + 35% of 600 = ? + 40% of 800

⇒ 120 + 210 = ? + 320

⇒ 330 = ? + 320

∴ ? = 10

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 

65% of 200 + 35% of 400 = ?

⇒ 130 + 140 = ?

∴ ? = 270

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 

45% of 300 - ? = 27 × 40 ÷ 9

⇒ 135 - ? = 120

⇒ 135 - 120 = ?

∴ ? = 15

Given:

132 ÷ 11 - 15 × 8 + 128 = ?

Concept:

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

 

Calculation:

132 ÷ 11 - 15 × 8 + 128 = ?

⇒ 12 - 15 × 8 + 128 = ?

⇒ 12 - 120 + 128 = ?

⇒ 12 - 120 + 128 = ?

⇒ 140 - 120 = ?

∴ ? = 20

Shortcut Trick

Principal (P) = ₹2500, Amount (A) = P + CI = 2500 + 749 = ₹3249.

Ratio A/P = 3249/2500 = (57/50)². Since the rate is 14%, multiplier is (1 + 14/100) = 114/100 = 57/50.

Power 2 implies Time (T) = 2 years.

Simple Interest = P × R × T / 100 = 2500 × 7% × 2 = 14% of 2500 = ₹350.

∴ The correct answer is ₹350.

Alternate Method

Given: Principal (P) = ₹2500, CI = ₹749, Rate (R₁) = 14%.

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

⇒ 2500 + 749 = 2500(1 + 14/100)^T

⇒ 3249/2500 = (114/100)^T

⇒ (57/50)² = (57/50)^T ⇒ T = 2 years.

⇒ New Rate (R₂) = 7%.

⇒ Simple Interest (SI) = (P × R₂ × T) / 100

⇒ SI = (2500 × 7 × 2) / 100 = 25 × 14

⇒ SI = ₹350.

∴ The correct answer is ₹350.

Additional Information

Compound Interest vs Simple Interest

For the first year (if compounded annually), SI and CI are equal. From the second year, CI > SI because interest is earned on previous interest.

Difference for 2 Years

The difference between CI and SI for 2 years is given by the formula: Difference = P(R/100)².

Effective Rate of Interest

The effective annual rate for CI for 2 years is x + y + (xy/100)%. For 14% it is 14 + 14 + (196/100) = 29.96%.

Shortcut Trick

Using M₁D₁ = M₂D₂: a(a − 19) = (a − 9)(a − 15)

a² − 19a = a² − 24a + 135 ⇒ 5a = 135 ⇒ a = 27

Total Work = 27 × (27 − 19) = 216 units

For twice the job (432 units) in 54 days: M = 432 ÷ 54 = 8

∴ The correct answer is 8 persons.

Alternate Method

Given: Case 1: a persons in (a − 19) days. Case 2: (a − 9) persons in (a − 15) days.

Formula Used: M₁ × D₁ / W₁ = M₂ × D₂ / W₂

⇒ a × (a − 19) = (a − 9) × (a − 15)

⇒ a² − 19a = a² − 15a − 9a + 135

⇒ a² − 19a = a² − 24a + 135

⇒ 24a − 19a = 135

⇒ 5a = 135 ⇒ a = 27

⇒ Total Work (W) = 27 × (27 − 19) = 27 × 8 = 216 units

⇒ New Work = 2 × 216 = 432 units

⇒ Number of persons = New Work ÷ Days = 432 ÷ 54

⇒ Number of persons = 8

∴ The correct answer is 8 persons.

Additional Information

Chain Rule Formula

The general formula is (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂, where M is men, D is days, H is hours, and W is work.

Work and Efficiency

Total work is directly proportional to the number of persons and time taken, assuming constant efficiency per person.

Inverse Proportion

For a constant amount of work, the number of persons required is inversely proportional to the number of days taken.

Shortcut Trick

New Average = Runs in last innings − [(Total innings − 1) × Increase in average]

New Average = 160 − [15 × 5]

New Average = 160 − 75 = 85 runs

∴ The correct answer is 85 runs.

Alternate Method

Given: Runs in 16^th innings = 160, Increase in average = 5.

Formula: Average = Total Runs ÷ Number of Innings

⇒ Let the average after 15 innings be x.

⇒ Total runs after 15 innings = 15 × x = 15x

⇒ Total runs after 16 innings = 15x + 160

⇒ New average = x + 5

⇒ Total runs = 16 × (x + 5) = 16x + 80

⇒ 15x + 160 = 16x + 80

⇒ 16x − 15x = 160 − 80

⇒ x = 80

⇒ Average after 16 innings = x + 5 = 80 + 5 = 85

∴ The correct answer is 85 runs.

Additional Information

Average Change Formula

New Average = Old Average + Change in Average. Also, Total increase = Number of terms × Increase in Average.

Batting Average

In cricket, batting average is Total Runs scored ÷ Number of times the batsman got out (usually treated as total innings in basic math problems).

Weighted Average

When two groups are combined, the new average A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Ratio of Length (L) × Breadth (B) = 8 × 7 = 56 units².

Value of 1 unit² = 224 ÷ 56 = 4.

Value of 1 unit = √4 = 2 cm.

Perimeter = 2 × (8 + 7) units = 2 × 15 units = 30 units.

Perimeter = 30 × 2 = 60 cm.

∴ The correct answer is 60 cm.

Alternate Method

Given:

Ratio of Length (L) to Breadth (B) = 8 : 7

Area of rectangle = 224 cm²

Formula Used:

Area = Length × Breadth

Perimeter = 2 × (Length + Breadth)

Calculations:

⇒ Let Length = 8x and Breadth = 7x

⇒ Area = 8x × 7x = 56x²

⇒ 56x² = 224

⇒ x² = 224 ÷ 56 = 4

⇒ x = √4 = 2

⇒ Length = 8 × 2 = 16 cm

⇒ Breadth = 7 × 2 = 14 cm

⇒ Perimeter = 2 × (16 + 14) = 2 × 30

⇒ Perimeter = 60 cm

∴ The correct answer is 60 cm.

Additional Information

Area and Perimeter of Rectangle

The Area is the product of adjacent sides (L × B), while Perimeter is the total boundary length 2(L + B).

Diagonal of Rectangle

The length of the diagonal (d) can be found using the Pythagorean theorem: d = √(L² + B²).

Square as a Special Case

When length equals breadth (L = B = a), the rectangle becomes a square with Area = a² and Perimeter = 4a.

Shortcut Trick

Let Total Distance XY be 20 units (LCM of 4 and 10).

Speed of A = 20 ÷ 10 = 2 units/hr.

Combined Speed (A + B) = 20 ÷ 4 = 5 units/hr.

Speed of B = 5 − 2 = 3 units/hr.

Time taken by B = 20 ÷ 3 = 6.67 hr.

∴ The correct answer is 6.67 hr.

Alternate Method

Given: Time for A to cover XY = 10 hr, Meeting time = 4 hr.

Formula Used: Speed = Distance ÷ Time; Relative Speed = S_A + S_B.

⇒ Let Distance XY = D.

⇒ Speed of Train A (S_A) = D/10.

⇒ In 4 hours, Train A covers distance = 4 × (D/10) = 0.4D.

⇒ In the same 4 hours, Train B covers the remaining distance = D − 0.4D = 0.6D.

⇒ Speed of Train B (S_B) = 0.6D / 4 = 0.15D.

⇒ Time taken by B to travel XY = D / 0.15D = 100/15 hr.

⇒ Time = 6.67 hr.

∴ The correct answer is 6.67 hr.

Additional Information

Relative Speed Concept

When two objects move towards each other, their Relative Speed is the sum of their individual speeds (S₁ + S₂).

Time and Distance Relation

For a constant distance, Speed is inversely proportional to Time (S ∝ 1/T). Ratio of speeds S_A:S_B is equal to the ratio of times T_B:T_A.

Meeting Point Formula

Meeting Time = (Total Distance) ÷ (Relative Speed). This applies when both start at the same time.

Shortcut Trick

Marks obtained = 30% of 150 = 45 marks.

Additional marks gained = 10% of present marks = 10% of 45 = 4.5 marks.

New total marks = 45 + 4.5 = 49.5 marks.

Since he passes by 1.5 marks at 49.5, Passing Marks = 49.5 − 1.5 = 48 marks.

∴ The correct answer is 48 marks.

Alternate Method

Given:

Maximum Marks = 150

Initial Score % = 30%

Increase % = 10% of present marks

Calculations:

⇒ Present marks = (30 ÷ 100) × 150 = 45 marks

⇒ Increase in marks = 10% of 45 = (10 ÷ 100) × 45 = 4.5 marks

⇒ Total marks obtained after increase = 45 + 4.5 = 49.5 marks

⇒ Passing marks = New marks − Surplus marks

⇒ Passing marks = 49.5 − 1.5 = 48 marks

∴ The correct answer is 48 marks.

Additional Information

Percentage Increase

To increase a value by x%, multiply the value by (1 + x/100). In this case, 10% more of 45 is 45 × 1.1 = 49.5.

Passing Percentage Formula

Passing Percentage = (Passing Marks ÷ Maximum Marks) × 100. For this problem, it would be (48 ÷ 150) × 100 = 32%.

Shortcut Trick

Total profit is assumed as LCM of 4 and 3, which is 12 units.

X's share = 1/4 × 12 = 3 units.

Y's share = 1/3 × 12 = 4 units.

Z's share = 12 − (3 + 4) = 5 units.

Given 5 units = Rs. 20,000 ⇒ 1 unit = Rs. 4,000.

Y's share = 4 units = 4 × 4,000 = Rs. 16,000.

∴ The correct answer is Rs. 16,000.

Alternate Method

Given → X receives 1/4 of profit, Y receives 1/3 of profit, Z receives Rs. 20,000.
Formulas → Total Profit = X + Y + Z | Share = Fraction × Total Profit.

⇒ Let total profit be P.
⇒ X + Y + Z = P.
⇒ (1/4)P + (1/3)P + 20,000 = P.
⇒ (3P + 4P)/12 + 20,000 = P.
⇒ 7P/12 + 20,000 = P.
⇒ P − 7P/12 = 20,000 ⇒ 5P/12 = 20,000.
⇒ P = (20,000 × 12) ÷ 5 = Rs. 48,000.
⇒ Y's share = (1/3) × 48,000 = Rs. 16,000.

∴ The correct answer is Rs. 16,000.

Additional Information

Partnership Profit Sharing

Profit is generally shared in the ratio of investment and time duration (Profit = Investment × Time).

Fractional Parts

The sum of all fractional shares in a partnership must always equal 1 (Total Whole).

Shortcut Trick

Speed ratio is inverse of Time ratio for constant distance.

Downstream Speed (D) : Upstream Speed (U) = 5 : 3

Ratio of Man speed (x) to Stream speed (y) = (5+3)/2 : (5−3)/2 = 4 : 1

Given y = 11 km/hr (1 unit), so x = 4 × 11 = 44 km/hr.

∴ The correct answer is 44 km/hr.

Alternate Method

Given: Downstream time (t_d) = 3 hours, Upstream time (t_u) = 5 hours, Stream speed (y) = 11 km/hr.

Formula Used: Distance = Speed × Time; Downstream speed = x + y; Upstream speed = x − y.

⇒ Let Speed of man in still water be x km/hr.

⇒ Distance downstream = 3 × (x + 11)

⇒ Distance upstream = 5 × (x − 11)

⇒ Since distances are equal: 3(x + 11) = 5(x − 11)

⇒ 3x + 33 = 5x − 55

⇒ 2x = 88

⇒ x = 44 km/hr

∴ The correct answer is 44 km/hr.

Additional Information

Speed Relations in Boats

Speed of man in still water (x) = (Downstream speed + Upstream speed) ÷ 2.

Stream Speed Formula

Speed of stream (y) = (Downstream speed − Upstream speed) ÷ 2.

Average Speed for Round Trip

Average speed = (Downstream speed × Upstream speed) ÷ Speed in still water.

The pattern of the series is as follows:-

Consecutive prime numbers are being added

⇒ 36 + 2 = 38

⇒ 38 + 3 = 41

⇒ 41 + 5 = 46

⇒ 46 + 7 = 53

⇒ 53 + 11 = 64

⇒ 64 + 13 = 77

∴ The value of ? is 77

Calculation:

The series follows the following pattern:

⇒ 11 × 1 + 1 = 12

⇒ 12 × 2 + 2 = 26

⇒ 26 × 3 + 3 = 81

⇒ 81 × 4 + 4 = 328

⇒ 328 × 5 + 5 = 1645

∴ The missing term in the series is 328

The pattern of the series is

6 × 3 + 1 = 19

19 × 3 + 2 = 59

59 × 3 + 3 = 180

180 × 3 + 4 = 544

544 × 3 + 5 = 1637

The series follows the following pattern:

4 × 1.5 = 6

6 × 2 = 12

12 × 2.5 = 30

30 × 3 = 90

90 × 3.5 = 315

∴ The required term will be 90

Calculation:

The logic behind the given series is as follows:

3600 ÷ 10 = 360

360 ÷ 10 = 36

36 ÷ 10 = 3.6

3.6 ÷ 10 = 0.36

∴ The value of '?' is 3.6.

Solution:

Number of officers working in company A is selected for promotion= 80 × 1/4 = 20

Number of Assistants working in company A selected for promotion = (70 - 20) = 50

Number of assistants who didn't get promotion = (100 - 50) = 50.

Solution:

Number of officers working in company E = 160

Number of officers working in company F = (160 + 20) = 180

Number of assistants working in company D = 140

Number of assistants working in company F = (140 + 30) = 170

Required difference = (180 - 170) = 10

Solution:

Number of officers working in company A =  80

Number of officers working in company B = 120

Number of assistants working in company B = 110

Number of assistants working in company C = 70

Required ratio = (80 + 120): (110 + 70) = 200: 180 = 10: 9