Quantitative Aptitude PYQs

Solution:

Number of officers working in D and E = (150 + 160) = 310

Total number of assistants working in all companies = (100 + 110 + 70 + 140 + 180) = 600

Required percentage = 310/600 × 100 = 51.6%

Solution:

Number of female officers working in company C = 90 × 1/3 = 30

Number of males officers working in company C = (90 - 30) = 60

Number of female assistants working in company C = 70 × 3/7 = 30

Number of male assistants working in company C = (70 - 30) = 40

Required sum = (60 + 40) = 100

Shortcut Trick

Total Votes = 7500

Valid Votes = 80% of 7500 = 6000

Winner got 55% of valid votes → Loser got 45% of valid votes

Other candidate votes = 45% of 6000 = 0.45 × 6000 = 2700

∴ The correct answer is 2700.

Alternate Method

Given:

Total number of votes = 7500

Percentage of invalid votes = 20%

Calculations:

⇒ Percentage of valid votes = 100% − 20% = 80%

⇒ Total valid votes = 80% of 7500 = (80/100) × 7500 = 6000

⇒ One candidate got 55% of valid votes.

⇒ The other candidate got = 100% − 55% = 45% of valid votes

⇒ Number of votes for the other candidate = 45% of 6000

⇒ Other candidate votes = (45/100) × 6000 = 45 × 60 = 2700

∴ The correct answer is 2700.

Additional Information

Election Base Values

In election problems, winner/loser percentages are usually calculated on Valid Votes unless specified as a percentage of Total Votes.

Successive Percentage Method

Required Value = Total × (Valid % / 100) × (Required Candidate % / 100). Here: 7500 × 0.80 × 0.45 = 2700.

Majority Margin

The margin of victory is the difference between winner and loser votes: (55% − 45%) = 10% of valid votes.

Shortcut Trick

Ratio of Profit is Investment × Time.

Let A investment be 3 and B investment be 1.

Annual profit is shared equally, so Profit A = Profit B = Profit C.

Profit B = 1 × 12 = 12 units. Thus, Profit C = 12 units.

C joins after x months, so C stays for (12 − x) months. Also A stays for x months.

Profit A = 3 × x = 12 ⇒ x = 4. Time for C = 12 − 4 = 8 months.

Investment C × 8 = 12 ⇒ C = 1.5. % of A = (1.5 ÷ 3) × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Given → Investment ratio A : B = 3 : 1, Annual profit ratio A : B : C = 1 : 1 : 1.
Formulas: Profit = Investment × Time | Investment = Profit ÷ Time.

⇒ Profit of B = 1 (investment) × 12 (months) = 12 units.
⇒ Since profits are equal, Profit of A = 12 units and Profit of C = 12 units.
⇒ For A: 3 × x = 12 ⇒ x = 4 months.
⇒ Time for C = 12 − x = 12 − 4 = 8 months.
⇒ Investment of C × 8 = 12 ⇒ Investment of C = 1.5 units.
⇒ Required % = (Investment of C ÷ Investment of A) × 100 = (1.5 ÷ 3) × 100 = 50%.

∴ The correct answer is 50%.

Additional Information

Partnership Ratio

In a partnership, the profit is distributed in the ratio of the product of capital and the time period for which the capital is invested.

Annual Profit Calculation

Annual profit implies a total time frame of 12 months. If a person joins after x months, their money is invested for (12 − x) months.

Shortcut Trick

Initial Ratio of Silver : Aluminium : Copper = 5 : 4 : 7

Total units in initial mixture = 5 + 4 + 7 = 16 units

Given, 16 units = 320 kg → 1 unit = 20 kg

New Ratio = 5 : 4 : 8 (Only Copper units change from 7 to 8)

Change in Copper = 8 − 7 = 1 unit → 20 kg

∴ The correct answer is 20 kg.

Alternate Method

Given: Initial weight = 320 kg, Initial Ratio = 5 : 4 : 7, Final Ratio = 5 : 4 : 8

⇒ Sum of ratio parts = 5 + 4 + 7 = 16

⇒ Quantity of 1 unit = 320 ÷ 16 = 20 kg

⇒ Initial Copper = (7 ÷ 16) × 320 = 140 kg

⇒ In new alloy, Silver (100 kg) and Aluminium (80 kg) remain constant.

⇒ Ratio 5 : 4 : 8 matches the constant parts (5 units = 100 kg, 4 units = 80 kg).

⇒ New Copper quantity = 8 units × 20 kg = 160 kg

⇒ Copper added = 160 − 140 = 20 kg

∴ The correct answer is 20 kg.

Additional Information

Constant Part Rule

When one component is added to a mixture, the quantities (or ratios) of the other components must remain constant. If the ratio values differ, multiply by a factor to equalize them.

Ratio to Quantity Conversion

Total Quantity = (Sum of ratio parts) × (Value of 1 unit). This is the fastest way to map weights to ratio differences.

Alligation in Mixtures

For two-component mixtures, the Alligation rule (Quantity 1 / Quantity 2 = Difference 2 / Difference 1) can also be used to find addition amounts.

Shortcut Trick

Let total quantity be 100 kg. Total CP = 100 × 200 = Rs. 20,000.

Desired SP = 20,000 × 1.25 = Rs. 25,000.

Remaining quantity = 80% of 100 = 80 kg.

Required SP per kg = 25,000 ÷ 80 = Rs. 312.5.

∴ The correct answer is Rs. 312.5.

Alternate Method

Given: CP = Rs. 200/kg, Rotten = 20%, Desired Profit = 25%.

Formulas: Total SP = Total CP × (100 + P%) ÷ 100 | Selling Price per kg = Total SP ÷ Available Quantity.

⇒ Let purchase be 1 kg. Total CP = Rs. 200.

⇒ Target Total Revenue = 200 × (125 ÷ 100) = Rs. 250.

⇒ Remaining usable weight = 1kg − (20% of 1kg) = 0.8 kg.

⇒ Selling Price per kg = 250 ÷ 0.8 = Rs. 312.5.

∴ The correct answer is Rs. 312.5.

Additional Information

Effective Cost Price

When goods are lost or rotten, the effective CP per unit increases. Effective CP = Total CP ÷ Net usable quantity.

Profit Calculation

Profit is always calculated on the initial Total Investment, regardless of how much quantity is lost or wasted during the process.

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 

75% of 500 + 40% of 650 = ?

⇒ (75/100) × 500 + (40/100) × 650 = ?

⇒ 375 + 260 = ?

∴ ? = 635

256 × 2^-5 × ? = (2/25) of 50 × 75

⇒ 2⁸ × 2^-5 × ? = (2/25) of 50 × 75

⇒ 2⁸ × 2^-5 × ? = (2/25) ×  50 × 75

⇒ 2⁸ × 2^-5 × ? = 2 ×  2 × 75

⇒ 2⁸/2⁵ × ? = 4 × 75

⇒ 8 × ? = 4 × 75

⇒ ? = 75/2

⇒ ? = 37.5

37% of 700 - 39% of 400 = ? - 31% of 300

⇒ 37 × 7 - 39 × 4 = ? - 31 × 3

As all unit digits in options are different, hence we can reach to answer by only calculating unit digits

⇒ 7 × 7 - 9 × 4 = ? - 1 × 3

⇒ ? = 9 - 6 + 3 = 6

Hence, answer will be 196

150% of 220 + 83 + 10% of ? = 302

⇒ 330 + 512 + ?/10 = 900

⇒ ?/10 = 900 - 330 - 512

⇒ ?/10 = 58

⇒ ? = 580

? + 308 - 25% of 4036 = 182​

⇒ ? + 308 - 4036/4 = 324

⇒ ? + 308 - 1009 = 324

⇒ ? = 1009 + 324 - 308

⇒ ? = 1025

20% of (28 × 40) - √? = 156 × 30 ÷ 26

⇒ 28 × 40/5 - √? = 6 × 30

⇒ 224 - √? = 180

⇒ √? = 224 - 180

⇒ √? = 44

⇒ ? = 1936

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 

80 – 42 ÷ 14 – 19 × 3 = ?

⇒ 80 – 3 – 19 × 3 = ?

⇒ 80 – 3 – 57 = ?

⇒ 80 – 60 = ?

∴ ? = 20

Given:

4532 ÷ √1936 + 524 ÷ 4 = ?

Concept:

Calculation:

⇒ 4532 ÷ 44 + 131 = ?

⇒ 103 + 131 = ?

⇒ 234 = ?

√676 × 34 + 125 × 7 = ? - 41

⇒ 26 × 34 + 125 × 7 = ? - 41

⇒ 884 + 875 = ? - 41

⇒ 1759 = ? - 41

⇒ ? = 1759 + 41 = 1800

Given:

(256 - 196 + 169 - 144) ÷ ? = 500

Concept used:

Calculation:

(256 - 196 + 169 - 144) ÷ ? = 500

⇒ (425 - 340) ÷ ? = 500

⇒ 85 ÷ ? = 500

⇒ ? = 0.17

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 400 + 35% of 600 = ?

⇒ 260 + 210 = ?

∴ ? = 470

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 

40% of 600 + ∛729 – 132 = ?

⇒ 240 + 9 – 169 = ?

⇒ 249 – 169 = ?

∴ ? = 80

24 × 16.67% + 36 × 11.11% + 42 × 14.28% = ?

⇒ 24 × 1/6 + 36 × 1/9 + 42 × 1/7 = ?

⇒ 4 + 4 + 6 = ?

⇒ ? = 14

35 × 25 + 55 × 45 + 75 × 65 = ? × 5

⇒ (30 + 5)(30 - 5) + (50 + 5)(50 - 5) + (70 + 5)(70 - 5) = ? × 5

⇒ 30² - 5² + 50² - 5² + 70² - 5² = ? × 5

⇒ 900 - 25 + 2500 - 25 + 4900 - 25 = ? × 5

⇒ (900 + 2500 + 4900) - (25) × 3 = ? × 5

⇒ 8300 - 75 = ? × ?

⇒ ? = 8225/5 = 1645