Quantitative Aptitude PYQs

Shortcut Trick

Observe the proportionality between the first group and the target group.

First Group: 5 men + 6 women → 12 days

Target Group: 15 men + 18 women = 3 × (5 men + 6 women)

Since the number of workers is multiplied by 3, the time taken will be divided by 3 (inverse proportion).

New Time = 12 ÷ 3 = 4 days.

∴ The correct answer is 4 days.

Alternate Method

Step 1: Find the relation between Men (M) and Women (W)

⇒ (5M + 6W) × 12 = (8M + 4W) × 8

⇒ (5M + 6W) × 3 = (8M + 4W) × 2

⇒ 15M + 18W = 16M + 8W

⇒ 1M = 10W

Step 2: Calculate Total Work in terms of Women

⇒ Total Work = (5 × 10W + 6W) × 12

⇒ Total Work = 56W × 12 = 672W

Step 3: Efficiency of 15 men and 18 women

⇒ Efficiency = 15M + 18W = 15 × (10W) + 18W = 150W + 18W = 168W

Step 4: Calculate Time Required

⇒ Time = Total Work ÷ Efficiency

⇒ Time = 672W ÷ 168W = 4 days

∴ The correct answer is 4 days.

Additional Information

Chain Rule Formula

The general formula is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is persons, D is days, H is hours, and W is work.

Inverse Proportionality

Time taken to complete a work is inversely proportional to the efficiency or the number of workers. If workers become 'n' times, time becomes 1/n.

Efficiency Comparison

To solve group work problems, always equate the total work (M₁D₁ = M₂D₂) to find the ratio of individual efficiencies.

Shortcut Trick

Upstream speed = 12 / 2 = 6 kmph.

Stream speed = Still water speed − Upstream speed = 16 − 6 = 10 kmph.

Downstream speed = Still water speed + Stream speed = 16 + 10 = 26 kmph.

Downstream time = 52 / 26 = 2 hours.

∴ The correct answer is 2 hr.

Alternate Method

Given:

Speed of boat in still water (u) = 16 kmph

Upstream distance = 12 km, Upstream time = 2 hours

Downstream distance = 52 km

Formula Used:

Speed = Distance ÷ Time

Upstream Speed (v_u) = u − v (where v is stream speed)

Downstream Speed (v_d) = u + v

⇒ Upstream speed = 12 / 2 = 6 kmph

⇒ 16 − v = 6

⇒ v = 16 − 6 = 10 kmph (Speed of stream)

⇒ Downstream speed = u + v = 16 + 10 = 26 kmph

⇒ Time to travel 52 km downstream = 52 / 26 = 2 hours

∴ The correct answer is 2 hr.

Additional Information

Still Water Speed Calculation

Still water speed (u) = 1/2 × (Downstream Speed + Upstream Speed).

Stream Speed Calculation

Stream speed (v) = 1/2 × (Downstream Speed − Upstream Speed).

Relative Speed Concept

In downstream, the stream helps the boat (add speeds); in upstream, the stream opposes the boat (subtract speeds).

Shortcut Trick

Ratio of saving (Kunal : Karan) = 1 : 3

Difference in ratio units = 3 − 1 = 2 units

Given 2 units = ₹28,000 ⇒ 1 unit = ₹14,000

Total saving (1 + 3) = 4 units = 4 × ₹14,000 = ₹56,000

∴ The correct answer is ₹56,000.

Alternate Method

Given: Saving ratio of Kunal and Karan = 1 : 3

Formula: Value of one unit = Actual Difference ÷ Difference in Ratio

⇒ Let saving of Kunal = 1x and Karan = 3x

⇒ 3x − 1x = 28,000

⇒ 2x = 28,000

⇒ x = 14,000

⇒ Total saving = 1x + 3x = 4x

⇒ Total saving = 4 × 14,000 = 56,000

∴ The correct answer is ₹56,000.

Additional Information

Ratio and Proportion Basics

If a : b is the ratio of two quantities, the total sum is represented by (a + b) units and the difference by |a − b| units.

Income, Expenditure and Saving Relation

Income = Expenditure + Savings. This fundamental formula is widely used in financial ratio problems.

Unitary Method in Ratios

To find the actual value of any part, divide the known total or difference by its corresponding ratio units to find the value of 1 unit.

Common Calculation

Calculation

Ratio of boys in 2021 and 2022 = 2:3;

Girls in 2022 are 10% less than boys.

Boys 2022 = 160 × (3/2) = 240

Girls 2022 = 240 × 0.9 = 216

Answer: 216 girls

Common Calculation

Calculation

Given: Difference between boys in 2020 and 2019 = 5x

Difference = 150 − 140 = 10

5x = 10 → x = 2

7x + 22 = 7 × 2 + 22 = 36

Answer: 36

Common Calculation

 

Calculation

Given: 1 teacher per 5 students

Total students 2019 = 110 + 140 = 250

Teachers = 250 ÷ 5 = 50

Answer: 50 teachers

Common Calculation

 

Calculation

Total students 2020 + 2018 = 280 + 250 = 530

Total boys 2021 + 2019 = 160 + 140 = 300

Ratio = 530 : 300 = 53 : 30

Answer: 53 : 30

Common Calculation

 

Calculation

Total boys = 120 + 140 + 150 + 160 = 570

Total girls = 130 + 110 + 130 + 180 = 550

Difference = 570 − 550 = 20

Answer: 20

Given:

1347 + 254 + 457 – 3382 + 8745 – 5723 = ?

Concept:

Calculation:

1347 + 254 + 457 – 3382 + 8745 – 5723 = ?

⇒ ? = 2058 + 5363 – 5723

⇒ ? = 7421 – 5723

∴ ? = 1698

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 

Now, we have

⇒ [{(48 ÷ 6 × 3 + 8) ÷ 4 × 5 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [{(8 × 3 + 8) ÷ 4 × 5 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [{(24 + 8) ÷ 4 × 5 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [{32 ÷ 4 × 5 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [{8 × 5 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [{40 – 8} × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [32 × 2 ÷ 4 × 4 + 1] – 3 = ?

⇒ [32 × (1/2) × 4 + 1] – 3 = ?

⇒ [64 + 1] – 3 = ?

⇒ 65 – 3 = ?

∴ ? = 62

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.

Given expression is,

⇒ (1333 - 339) ÷ 2 + 103 = 21 × 39 - ?

⇒ 994 ÷ 2 + 103 = 21 × 39 - ?

⇒ 497 + 103 = 819 - ?

⇒ 600 = 819 - ?

⇒ ? = 819 - 600

⇒ ? = 219

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.

Given expression is,

⇒ 7859 - 1109 + 335 = 20 + 785 × ?

⇒ 8194 - 1109 = 20 + 785 × ?

⇒ 7085 = 20 + 785 × ?

⇒ 7085 - 20 = 785 × ?

⇒ 7065 = 785 × ?

⇒ ? = 7065/785

⇒ ? = 9

Given:

[(27 × 10) ÷ 30 + 10500 ÷ 500] = ? × 15

Concept Used:

Calculation:

Suppose x will come in the place of the question mark;

[(27 × 10) ÷ 30 + 10500 ÷ 500] = x × 15

Applying BODMAS Rule;

⇒ [(270) ÷ 30 + 21] = 15x

⇒ 9 + 21 = 15x

⇒ 30 = 15x

∴ x = 2

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.

Given expression is,

⇒ {(3654 + 1346) × 2} ÷ 200 = ?

⇒ {(5000) × 2} ÷ 200 = ?

⇒ ? = 10000 ÷ 200

⇒ ? = 50

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.

Given expression is,

⇒ 579 × 4 + 184 = 1388 ÷ ? + 1112

⇒ 2316 + 184 = 1388 ÷ ? + 1112

⇒ 2500 = 1388 ÷ ? + 1112

⇒ 2500 – 1112 = 1388 ÷ ?

⇒ 1388 = 1388 ÷ ?

⇒ ? = 1

Suppose x will come in place of question mark;

5350 – 50 × 3139 ÷ 73 = x × 64

Applying BODMAS Rule;

⇒ 5350 – 50 × 43 = 64x

⇒ 5350 – 2150 = 64x

⇒ 3200 = 64x

⇒ x = 50

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

Step - 1 - steps of an equation enclosed in ‘Brackets’ must be solved first.

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.

Now, the given expression:

⇒ (224 ÷ 16 × 33) ÷ 21 = 2 × (? + 3)

⇒ (14 × 33) ÷ 21 = 2 × (? + 3)

⇒ 462 ÷ 21 = 2 × ? + 6

⇒ 22 = 2 × ? + 6

⇒ 2 × ? = 22 - 6

⇒ 2 × ? = 16

⇒ ? = 8

Shortcut Trick

Effective Rate of Interest for 2 years at 2% = r + r + (r × r)/100 = 2 + 2 + (2 × 2)/100 = 4.04%.

Given Compound Interest (CI) = ₹323.2.

Equating percentage to value: 4.04% of Principal = ₹323.2.

Principal = 323.2 ÷ 0.0404 = ₹8,000.

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Time (T) = 2 years

Rate (R) = 2% per annum

Compound Interest (CI) = ₹323.2

Formula Used:

CI = P[(1 + R/100)^T − 1]

Calculations:

⇒ 323.2 = P[(1 + 2/100)² − 1]

⇒ 323.2 = P[(1.02)² − 1]

⇒ 323.2 = P[1.0404 − 1]

⇒ 323.2 = P × 0.0404

⇒ P = 323.2 ÷ 0.0404

⇒ P = 3232000 ÷ 404

⇒ P = ₹8,000

∴ The correct answer is ₹8,000.

Additional Information

Effective Interest Rate

For 2 years, the net effective rate for CI is given by x + y + (xy/100). For 2%, it is 2 + 2 + 0.04 = 4.04%.

Difference between CI and SI

The difference for 2 years is P(R/100)². Here, the difference would be ₹8000 × (0.0004) = ₹3.2.

Amount Formula

Total Amount (A) = Principal (P) + Compound Interest (CI). Also, A = P(1 + R/100)^T.

Shortcut Trick

Proportion of alcohol in Mixture 1 = 7/10 and Mixture 2 = 3/8.

Mixed in ratio 3 : 4 → Total parts = 3 + 4 = 7 units.

Total alcohol in 7 units = [3 × (7/10)] + [4 × (3/8)] = 2.1 + 1.5 = 3.6 units.

Alcohol fraction in final mix = 3.6 / 7.

Alcohol in 70 litres = (3.6 / 7) × 70 = 36 litres.

∴ The correct answer is 36 litres.

Alternate Method

Given: Ratio in Mix 1 = 7 : 3, Ratio in Mix 2 = 3 : 5, Mixing ratio = 3 : 4, Total quantity = 70 litres.

Formula: Total Alcohol = Σ(Quantity × Alcohol Fraction)

⇒ Quantity of Mix 1 = [3 / (3 + 4)] × 70 = 30 litres.

⇒ Quantity of Mix 2 = [4 / (3 + 4)] × 70 = 40 litres.

⇒ Alcohol from Mix 1 = 30 × (7 / (7 + 3)) = 30 × (7/10) = 21 litres.

⇒ Alcohol from Mix 2 = 40 × (3 / (3 + 5)) = 40 × (3/8) = 15 litres.

⇒ Total Alcohol = 21 + 15 = 36 litres.

∴ The correct answer is 36 litres.

Additional Information

Alligation Method

Used to find the ratio in which two ingredients at given prices/concentrations must be mixed to produce a mixture of a desired price/concentration.

Fractional Mixing

When mixing two ratios A:B and C:D in ratio m:n, ensure the sum of parts (A+B and C+D) are made equal or scaled to m and n respectively before adding.

Calculation

Sunday total = 84 + 55 + 64 = 203

Monday total = 48 + 32 + 32 = 112

Difference = 203 – 112 = 91