Quantitative Aptitude

Percentage

482 Questions
All Successive Percentage Changes 177 Population Growth and Depreciation 103 Fractional Base Multiplication 58 Reverse More-Than and Less-Than Comparisons 38 Income, Expenditure, and Savings 33 Price and Consumption 30 Election Votes and Margins 10 Fake Weight and Faulty Measures 10 Venn Diagram Percentages 9 Passing Marks Shifts 5 Fresh vs. Dry Mixture 2

Percentage Questions

Multiple choice

The weight of two persons N and A are in the ratio of 4 : 5. A's weight increased by 20% and the total weight of N and A together became 135 kg with an increase of 25%. By what percent did the weight of N increase?

  1. 28.75%

  2. 32.25%

  3. 31.25%

  4. 33.25%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial weights be 4x and 5x (total 9x). After 25% increase, new total is 135 kg, so original total = 135/1.25 = 108 kg. Therefore 9x = 108, x = 12. Initial: N = 48 kg, A = 60 kg. A's new weight = 60 × 1.2 = 72 kg. New total = 135 kg, so N's new weight = 135 - 72 = 63 kg. N's increase = 63 - 48 = 15 kg. Percentage increase = (15/48) × 100 = 31.25%.

Multiple choice

A shopkeeper bought an article marked at Rs. 22800 at two successive discounts of 15% and 20%. He spent Rs. 1064 on transportation and sold the article for Rs. 20710. Then, what was the profit percentage of the shopkeeper?

  1. 35%

  2. 30%

  3. 25%

  4. 20%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First calculate purchase price after successive discounts: ₹22,800 × 0.85 × 0.80 = ₹15,504. Total cost including transportation: ₹15,504 + ₹1,064 = ₹16,568. Profit: ₹20,710 - ₹16,568 = ₹4,142. Profit percentage: (4,142 / 16,568) × 100 = 25%. The image dependence flag is incorrect as no image is needed.

Multiple choice

Divya went to a textile shop. When Divya asked the price of a saree the shopkeeper told her the price by increasing 18% of the original cost. But Divya insisted to decrease the price by 18% so the shopkeeper sold it by decreasing the price by 18% what is the loss or profit percent of shopkeeper?

  1. 3.25%

  2. 2.5%

  3. 3%

  4. 3.225%

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let original price = 100. Shopkeeper's selling price = 100 + 18% = 118. Then he reduces by 18%: 118 - 18% of 118 = 118 - 21.24 = 96.76. Loss = 100 - 96.76 = 3.24. Loss percent = 3.24/100 × 100 = 3.24%. This loss percentage doesn't match any of options A (3.25%), B (2.5%), C (3%), or D (3.225%). Therefore, the correct answer is E (None of these).

Multiple choice

Arbind spends 75% of his income and saves the rest. His income is increased by 20% and he increased his expenditure by 10%. Then the increase in savings in percentage is -

  1. 55%

  2. 52%

  3. 50%

  4. 48%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial income = 100. Initial expenditure = 75, savings = 25. New income = 120. New expenditure = 75 × 1.1 = 82.5. New savings = 120 - 82.5 = 37.5. Increase in savings = 37.5 - 25 = 12.5. Percentage increase = (12.5/25) × 100 = 50%.

Multiple choice

A student gets 20% marks and fails by 60 marks. Another student gets 32% marks and so he gets 84 marks more than passing marks. Find the percentage passing marks.

  1. 32 %

  2. 35 %

  3. 25%

  4. 40 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total marks = T and passing marks = P. First student: 20% of T = P - 60. Second student: 32% of T = P + 84. Subtracting first equation from second: 12% of T = 144, so T = 1200. Then P = 0.20 × 1200 + 60 = 240 + 60 = 300. Passing percentage = (300/1200) × 100 = 25%. The key insight is that 32% - 20% = 12% represents the difference between 84 marks above passing and 60 marks below passing.

Multiple choice

The population of a state increased from 100 million to 169 million in two decades. What is the average increase in population per decade?

  1. 20%

  2. 34.5%

  3. 69%

  4. 30%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total percentage increase = [(169 - 100) / 100] × 100 = 69%. This increase occurred over 2 decades. Average increase per decade = Total increase / Number of decades = 69% / 2 = 34.5%. Option C is the total increase over both decades, while option D is not the correct average. The calculation requires dividing the total increase evenly across the time period.

Multiple choice

The production of company A increased by 25% from 1994 to 1995, and its further increased by 60% from 1995 to 1996. What is the total percent increase in production from 1994 to 1996?

  1. 65%

  2. 75%

  3. 85%

  4. 100%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When production increases by 25% and then by 60%, the total increase is calculated multiplicatively: if 1994=100, then 1995=125 (100+25%), and 1996=200 (125+60% of 125). Total increase from 1994 to 1996 is 100%, not 85% (which would be 25+60).

Multiple choice

The population of a town increases at the rate of 15% per annum. If the present population is 108445 of town, then what was the population 2 years ago? एक शहर की जनसंख्या प्रति वर्ष 15% की दर से बढ़ती है। यदि शहर की वर्तमान जनसंख्या 108445 है, तो 2 वर्ष पहले आबादी क्या थी?

  1. 72000

  2. 79000

  3. 82000

  4. 85000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Present population = 108445. Let population 2 years ago = P. P × (1 + 15/100)² = 108445. P × 1.3225 = 108445. P = 108445/1.3225 ≈ 82000. For backward calculation with growth rate, divide present value by (1 + rate)ⁿ.

Multiple choice

The income of Raju is 20% more than his expenditure. If his income increases by 60% and his expenditure is increase by 70% then by what percent does his saving increases/decreases?

  1. It decreases by 10

  2. It decreases by 2%

  3. It increases by 10%

  4. It increases by 2%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let expenditure = E. Then income = 1.2E and savings = 0.2E. After 60% increase in income: new income = 1.6×1.2E = 1.92E. After 70% increase in expenditure: new expenditure = 1.7E. New savings = 1.92E-1.7E = 0.22E. Percentage change = (0.22E-0.2E)/(0.2E)×100 = 10%.

Multiple choice

Mr. Anurag buys goods at Himachal Pradesh at a discount of 20% on marked price. He has to pay certain kind of duties of 15% on the net cost he paid for goods bought. He marked a new price and earned a profit of 40% over his total expenses. What is the percentage change in the marked price?

  1. 32.20%

  2. 28.80%

  3. 30%

  4. 26.75%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original marked price = M. Anurag pays 80% of M (20% discount), plus 15% duty = 0.8M × 1.15 = 0.92M total cost. He earns 40% profit on this cost, so selling price = 1.4 × 0.92M = 1.288M. New marked price is 128.8% of original, an increase of 28.8%, confirming option B.

Multiple choice

In a shopping mall the cost of an article was increased by 10% and then it was decreased by 10%. The net increase or decrease percent is:

  1. 1.5% decrease

  2. 1% decrease

  3. 1.5% increase

  4. 1% increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If original price is P, after 10% increase: P × 1.1 = 1.1P. After 10% decrease: 1.1P × 0.9 = 0.99P. The final price is 0.99P, which is 1% less than the original P. This is a classic example of how percentage increases and decreases are not symmetric - a 10% decrease on 110% of original doesn't return to 100%.

Multiple choice

The price of the petrol is increased by 19% and Sunita intended to spend only an additional 12% on petrol. By what percent should she reduce the quantity of petrol purchased ( nearest to integer)

  1. 7

  2. 6

  3. 5

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When price increases by 19%, new price = 1.19 × original. To spend only 12% more, new spend = 1.12 × original spend. Let new quantity be q': 1.19P × q' = 1.12P × q, so q' = 1.12/1.19 ≈ 0.941. Reduction = 1 - 0.941 = 0.059 or 5.9% ≈ 6%.

Multiple choice

An article having marked price, Rs.900, was sold for Rs.648 after two successive discounts. The first discount was 20%. What was the percentage rate of the second discount?

  1. 5

  2. 15

  3. 10

  4. 12.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the second discount be d%. First discount 20% on Rs.900 gives 900 × 0.8 = Rs.720. Second discount d% on Rs.720 gives 720 × (1 - d/100) = Rs.648. So (1 - d/100) = 648/720 = 0.9, giving d/100 = 0.1 or d = 10%. Option C is correct. Option A (5%) would give 720 × 0.95 = Rs.684, B (15%) would give 720 × 0.85 = Rs.612, and D (12.5%) would give 720 × 0.875 = Rs.630.