Question 1

1. A man spends 40% of his monthly salary on house rent and 20% of the remaining on travel. Out of the remaining, he spends 10% on clothes and saves the rest. If his savings are Rs. 6,480, what is his total monthly salary?

A) Rs. 12,000B) Rs. 14,500C) Rs. 15,000D) Rs. 16,000

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let total salary be x. After rent (40%), remaining = 0.60x. After travel (20% of remaining), remaining = $0.60x \times 0.80 = 0.48x$. After clothes (10% of remaining), remaining (savings) = $0.48x \times 0.90 = 0.432x$. Given: 0.432x = 6480 $x = \frac{6480}{0.432} = 15,000$. Correct Answer: Rs. 15,000

Question 2

2. Two numbers are 32% and 20% less than a third number, respectively. What percentage is the first number of the second number?

80%

Question 3

3. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?

A) 40 kgB) 32 kgC) 50 kgD) 42 kg

Answer

✓ Correct Answer: Option A

Explanation: Solution: The pulp content remains constant in both fresh and dry fruit. In fresh fruit, pulp = (100 - 68)% = 32%. In 100 kg fresh fruit, pulp = 32 kg. Let x be the weight of dry fruit. In dry fruit, pulp = (100 - 20)% = 80%. So, 80% of x = 32 $0.80x = 32 ⇒ x = \frac{32}{0.8} = 40 kg$. Correct Answer: 40 kg

Question 4

4. The price of petrol is increased by 25%. By how much percentage should a car owner reduce his consumption of petrol so that his expenditure on petrol increases by only 10%?

A) 15%B) 10%C) 12.5%D) 12%

Answer

✓ Correct Answer: Option D

Explanation: Solution: Let original Price = 100 and original Consumption = 100. Original Expenditure = $100 \times 100 = 10,000$. New Price = 125. New target Expenditure = $10,000 \times 1.10 = 11,000$. New Consumption = $\frac{11000}{125} = 88$. Reduction in consumption = 100 - 88 = 12%. Correct Answer: 12%

Question 5

5. In an election between two candidates, 10% of the voters did not cast their votes and 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1,620 votes. The total number of voters enrolled on the voters' list was:

A) 20,000B) 25,000C) 30,000D) 35,000

Answer

✓ Correct Answer: Option B

Explanation: Solution: Let total voters = x. Votes polled = 0.90x. Valid votes = $0.90x \times 0.90 = 0.81x$. Winner got 54% of valid votes, so Loser got (100-54) = 46% of valid votes. Margin = (54 - 46)% = 8% of valid votes. 8% of 0.81x = 1620 $0.08 \times 0.81x = 1620$ $0.0648x = 1620 ⇒ x = \frac{1620}{0.0648} = 25,000$. Correct Answer: 25,000

Question 6

6. The population of a town increases by 5% annually. If its present population is 9,261, what was it 3 years ago?

A) 7,500B) 8,200C) 8,000D) 8,500

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let the population 3 years ago be P. $P(1 + \frac{5}{100})^3 = 9261$ $P(\frac{21}{20})^3 = 9261$ $P \times \frac{9261}{8000} = 9261$ P = 8,000. Correct Answer: 8,000

Question 7

7. If the income tax is increased by 19%, the net income is reduced by 1%. The rate of income tax is:

A) 5%B) 4%C) 6%D) 7.5%

Answer

✓ Correct Answer: Option A

Explanation: Solution: Decrease in Net Income = Increase in Tax. 1% of Net Income = 19% of Tax $\frac{Tax}{Net Income} = \frac{1}{19}$ Total Income = Tax + Net Income = 1 + 19 = 20. Rate of Tax = $(\frac{Tax}{Total Income} \times 100)% = (\frac{1}{20} \times 100)% = 5%$. Correct Answer: 5%

Question 8

8. In a certain examination, a candidate answered 25 questions and faced a scoring system where he got 100% marks for every correct answer but lost 10% of the marks of a correct answer for every wrong answer. If he scored 78% in total, how many questions did he answer correctly?

A) 18B) 22C) 19D) 20

Answer

✓ Correct Answer: Option D

Explanation: Solution: Let marks for 1 correct answer = 10. Marks for 1 wrong answer = -1. Total marks possible = $25 \times 10 = 250$. Actual marks = 78% of 250 = 195. Let c be correct answers and w be wrong answers. c + w = 25 (i) 10c - w = 195 (ii) Adding (i) and (ii): 11c = 220 ⇒ c = 20. Correct Answer: 20

Question 9

9. If A's income is 20% more than B's, and B's income is 25% less than C's, then by what percentage is A's income less than C's?

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

Answer

✓ Correct Answer: Option B

Explanation: Solution: Let C = 100. B = 100 - 25 = 75. A = 75 + (20% of 75) = 75 + 15 = 90. A is 10 less than C. Required percentage = $(\frac{10}{100} \times 100)% = 10%$. Correct Answer: 10%

Question 10

10. A solution of salt and water contains 5% salt. If 20 litres of water is evaporated, the salt becomes 15%. Find the initial quantity of the solution.

A) 25 litresB) 40 litresC) 30 litresD) 35 litres

Answer

✓ Correct Answer: Option C

Explanation: Solution: Salt remains constant. Let initial volume be V. Salt = 0.05V. New volume = V - 20. Salt = 0.15(V - 20). 0.05V = 0.15(V - 20) V = 3(V - 20) V = 3V - 60 2V = 60 ⇒ V = 30 litres. Correct Answer: 30 litres

Accepted Answer

✓ Correct Answer: Option B

Explanation: Solution: Let the third number be 100. First number = 100 - 32 = 68. Second number = 100 - 20 = 80. Required percentage = $(\frac{68}{80} \times 100)%$ $= (\frac{17}{20} \times 100)% = 85%$. Correct Answer: 85%

Quantitative Aptitude - Percentage (Set 4)

1. A man spends 40% of his monthly salary on house rent and 20% of the remaining on travel. Out of the remaining, he spends 10% on clothes and saves the rest. If his savings are Rs. 6,480, what is his total monthly salary?

2. Two numbers are 32% and 20% less than a third number, respectively. What percentage is the first number of the second number?

3. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?

4. The price of petrol is increased by 25%. By how much percentage should a car owner reduce his consumption of petrol so that his expenditure on petrol increases by only 10%?

5. In an election between two candidates, 10% of the voters did not cast their votes and 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1,620 votes. The total number of voters enrolled on the voters' list was:

6. The population of a town increases by 5% annually. If its present population is 9,261, what was it 3 years ago?

7. If the income tax is increased by 19%, the net income is reduced by 1%. The rate of income tax is:

8. In a certain examination, a candidate answered 25 questions and faced a scoring system where he got 100% marks for every correct answer but lost 10% of the marks of a correct answer for every wrong answer. If he scored 78% in total, how many questions did he answer correctly?

9. If A's income is 20% more than B's, and B's income is 25% less than C's, then by what percentage is A's income less than C's?

10. A solution of salt and water contains 5% salt. If 20 litres of water is evaporated, the salt becomes 15%. Find the initial quantity of the solution.