Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

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) $Rs. 12,000$

B) $Rs. 14,500$

C) $Rs. 15,000$

D) $Rs. 16,000$

Answer

Correct Answer: C

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?

A) $80\%$

B) $85\%$

C) $90\%$

D) $75\%$

Answer

Correct Answer: B

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%

Question 3

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

A) $40 \text{ kg}$

B) $32 \text{ kg}$

C) $50 \text{ kg}$

D) $42 \text{ kg}$

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: D

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) $20,000$

B) $25,000$

C) $30,000$

D) $35,000$

Answer

Correct Answer: B

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. $8\% \text{ of } 0.81x = 1620$ $0.08 \times 0.81x = 1620$ $0.0648x = 1620 \implies x = \frac{1620}{0.0648} = 25,000$. 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) $7,500$

B) $8,200$

C) $8,000$

D) $8,500$

Answer

Correct Answer: C

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: A

Solution: Decrease in Net Income = Increase in Tax. $1\% \text{ of Net Income} = 19\% \text{ of Tax}$ $\frac{\text{Tax}}{\text{Net Income}} = \frac{1}{19}$ Total Income = Tax + Net Income = $1 + 19 = 20$. Rate of Tax = $(\frac{\text{Tax}}{\text{Total Income}} \times 100)\% = (\frac{1}{20} \times 100)\% = 5\%$. 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) $18$

B) $22$

C) $19$

D) $20$

Answer

Correct Answer: D

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

Solution: Let $C = 100$. $B = 100 - 25 = 75$. $A = 75 + (20\% \text{ of } 75) = 75 + 15 = 90$. $A$ 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 $20 \text{ litres}$ of water is evaporated, the salt becomes $15\%$. Find the initial quantity of the solution.

A) $25 \text{ litres}$

B) $40 \text{ litres}$

C) $30 \text{ litres}$

D) $35 \text{ litres}$

Answer

Correct Answer: C

Solution: Salt remains constant. Let initial volume be $V$. Salt = $0.05V$. New volume = $V - 20$. Salt = $0.15(V - 20)$. $0.05V = 0.15(V - 20)$ $V = 3(V - 20)$ $V = 3V - 60$ $2V = 60 \implies V = 30 \text{ litres}$. Correct Answer: 30 litres

Accepted Answer

Correct Answer: A

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

Competitive Exams : Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

Competitive Exams : Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

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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 $20 \text{ litres}$ of water is evaporated, the salt becomes $15\%$. Find the initial quantity of the solution.

Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

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 $100 \text{ kg}$ of fresh fruits?

Competitive Exams : Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

Competitive Exams : Quantitative Aptitude - Percentage (Set 4) | Concept of Maths

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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 $20 \text{ litres}$ of water is evaporated, the salt becomes $15\%$. Find the initial quantity of the solution.