Question 1

1. The population of a town increases by 15% in the first year and decreases by 10% in the second year. If the current population is 20,700, what was the population two years ago?

A) 18,000B) 20,000C) 21,500D) 19,000

Answer

✓ Correct Answer: Option B

Explanation: Solution: Let the population two years ago be P. After 1st year: $P \times (1 + \frac{15}{100}) = P \times 1.15$ After 2nd year: $(P \times 1.15) \times (1 - \frac{10}{100}) = 20,700$ $P \times 1.15 \times 0.9 = 20,700$ $P \times 1.035 = 20,700$ $P = \frac{20,700}{1.035} = 20,000$.

Question 2

2. The price of sugar rises by 25%. By what percentage should a household reduce its consumption of sugar so that their expenditure on sugar increases by only 10%?

15%

Question 3

3. In an election between two candidates, 10% of the voters did not cast their votes. 10% of the votes cast were found invalid. The winning candidate got 54% of the valid votes and won by a majority of 1,620 votes. Find the total number of voters enrolled?

A) 25,000B) 20,000C) 30,000D) 22,500

Answer

✓ Correct Answer: Option A

Explanation: Solution: Let total voters = x. Votes cast = 0.9x. Valid votes = $0.9 \times 0.9x = 0.81x$. Winner got 54% of valid votes, so Loser got 46%. Difference = (54 - 46)% of 0.81x = 8% of 0.81x. $0.08 \times 0.81x = 1,620$ $0.0648x = 1,620 \Rightarrow x = \frac{1,620}{0.0648} = 25,000$.

Question 4

4. A man spends 75% of his income. His income increases by 20% and his expenditure increases by 10%. By what percentage do his savings increase?

A) 30%B) 40%C) 25%D) 50%

Answer

✓ Correct Answer: Option D

Explanation: Solution: Let Income = 100, Expenditure = 75, Savings = 25. New Income = 120. New Expenditure = $75 \times 1.10 = 82.5$. New Savings = 120 - 82.5 = 37.5. Increase in savings = 37.5 - 25 = 12.5. % increase = $(\frac{12.5}{25}) \times 100 = 50%$.

Question 5

5. In an examination, a candidate scoring 30% marks fails by 15 marks, while another candidate who scores 40% marks gets 35 marks more than the minimum pass marks. What is the passing percentage?

A) 35%B) 42%C) 33%D) 38%

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let total marks be M. 0.30M + 15 = 0.40M - 35 0.10M = 50 \Rightarrow M = 500. Pass marks = 0.30(500) + 15 = 150 + 15 = 165. Pass percentage = $(\frac{165}{500}) \times 100 = 33%$.

Question 6

6. A vessel contains 40 liters of a mixture of milk and water, containing 10% water. How much water should be added to make it 20% water in the new mixture?

A) 5 litersB) 4 litersC) 8 litersD) 10 liters

Answer

✓ Correct Answer: Option A

Explanation: Solution: Initial water = 10% of 40 = 4 liters. Milk = 36 liters. In the new mixture, milk (36 liters) will be 80% (since water is 20%). 80% of New Total = 36. New Total = \frac{36}{0.8} = 45$ liters. Water added = 45 - 40 = 5 liters.

Question 7

7. The sales tax on an item is reduced by 20%, and its consumption increases by 15%. What is the overall percentage effect on the revenue collected?

A) 5% increaseB) 8% decreaseC) 10% decreaseD) 4% increase

Answer

✓ Correct Answer: Option B

Explanation: Solution: Revenue = Tax Rate $\times$ Consumption. Let initial Revenue = $100 \times 100 = 10,000$. New Tax Rate = 80. New Consumption = 115. New Revenue = $80 \times 115 = 9,200$. Decrease = 10,000 - 9,200 = 800. % change = $(\frac{-800}{10,000}) \times 100 = -8%$.

Question 8

8. If A is 20% more than B, and B is 25% less than C, then by what percentage is A less than C?

A) 5%B) 12%C) 10%D) 15%

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let C = 100. B = 100 - 25% = 75. A = 75 + 20% of 75 = 75 + 15 = 90. Difference between C and A = 100 - 90 = 10. A is 10% less than C.

Question 9

9. In a survey, it was found that 60% of people like Tea, 50% like Coffee, and 10% like neither. What percentage of people like both?

A) 10%B) 30%C) 15%D) 20%

Answer

✓ Correct Answer: Option D

Explanation: Solution: Total people = 100%. People who like at least one = 100% - 10% = 90%. Using $n(A \cup B) = n(A) + n(B) - n(A \cap B)$: 90% = 60% + 50% - n(Both) n(Both) = 110% - 90% = 20%.

Question 10

10. If the length of a rectangle is increased by 40% and the breadth is decreased by 20%, find the percentage change in its area.

A) 10% increaseB) 12% increaseC) 20% increaseD) 8% decrease

Answer

✓ Correct Answer: Option B

Explanation: Solution: Area = $L \times B$. Using successive percentage formula: $x + y + \frac{xy}{100}$ x = +40, y = -20 Change = $40 - 20 + \frac{(40)(-20)}{100}$ Change = 20 - 8 = +12%. Area increases by 12%.

Accepted Answer

✓ Correct Answer: Option C

Explanation: Solution: Let initial Price be 100 and initial Consumption be 100. Initial Expenditure = 10,000. New Price = 125. Target Expenditure = $10,000 \times 1.10 = 11,000$. New Consumption = \frac{11,000}{125} = 88. Reduction in consumption = 100 - 88 = 12%.

Competitive Exams : Quantitative Aptitude - Percentage (Set 2)

1. The population of a town increases by 15% in the first year and decreases by 10% in the second year. If the current population is 20,700, what was the population two years ago?

2. The price of sugar rises by 25%. By what percentage should a household reduce its consumption of sugar so that their expenditure on sugar increases by only 10%?

3. In an election between two candidates, 10% of the voters did not cast their votes. 10% of the votes cast were found invalid. The winning candidate got 54% of the valid votes and won by a majority of 1,620 votes. Find the total number of voters enrolled?

4. A man spends 75% of his income. His income increases by 20% and his expenditure increases by 10%. By what percentage do his savings increase?

5. In an examination, a candidate scoring 30% marks fails by 15 marks, while another candidate who scores 40% marks gets 35 marks more than the minimum pass marks. What is the passing percentage?

6. A vessel contains 40 liters of a mixture of milk and water, containing 10% water. How much water should be added to make it 20% water in the new mixture?

7. The sales tax on an item is reduced by 20%, and its consumption increases by 15%. What is the overall percentage effect on the revenue collected?

8. If A is 20% more than B, and B is 25% less than C, then by what percentage is A less than C?

9. In a survey, it was found that 60% of people like Tea, 50% like Coffee, and 10% like neither. What percentage of people like both?

10. If the length of a rectangle is increased by 40% and the breadth is decreased by 20%, find the percentage change in its area.