Competitive Exams : Quantitative Aptitude - Percentage (Set 1) | Concept of Maths

Question 1

1. A man spends $75\%$ of his income. His income increases by $20\%$ and his expenditure increases by $10\%$. Find the percentage increase in his savings.

A) $30\%$

B) $40\%$

C) $50\%$

D) $60\%$

Answer

Correct Answer: C

Let Initial Income = $100$. Expenditure = $75$, Savings = $100 - 75 = 25$. New Income = $100 + 20\% \text{ of } 100 = 120$. New Expenditure = $75 + 10\% \text{ of } 75 = 75 + 7.5 = 82.5$. New Savings = $120 - 82.5 = 37.5$. Increase in Savings = $37.5 - 25 = 12.5$. Percentage Increase = $(\frac{12.5}{25}) \times 100 = 50\%$.

Question 2

2. The population of a town was $1,60,000$ three years ago. If it increased by $5\%$, $10\%$, and $15\%$ in the last three years respectively, what is the present population?

A) $2,10,520$

B) $2,12,520$

C) $2,08,420$

D) $2,15,600$

Answer

Correct Answer: B

Present Population = $1,60,000 \times (1 + \frac{5}{100}) \times (1 + \frac{10}{100}) \times (1 + \frac{15}{100})$ = $1,60,000 \times \frac{105}{100} \times \frac{110}{100} \times \frac{115}{100}$ = $160 \times 1.05 \times 1.10 \times 115 = 2,12,520$.

Question 3

3. In an examination, a student had to obtain $33\%$ of the maximum marks to pass. He got $125$ marks and failed by $40$ marks. The maximum marks were:

A) $500$

B) $600$

C) $800$

D) $1000$

Answer

Correct Answer: A

Passing Marks = Marks obtained + Marks failed by Passing Marks = $125 + 40 = 165$. According to the question, $33\%$ of Total Marks = $165$. Total Marks = $\frac{165 \times 100}{33} = 5 \times 100 = 500$.

Question 4

4. $40$ litres of a mixture of milk and water contains $10\%$ water. How much water should be added to make the water $20\%$ in the new mixture?

A) $4$ litres

B) $10$ litres

C) $8$ litres

D) $5$ litres

Answer

Correct Answer: D

Initial water = $10\% \text{ of } 40 = 4$ litres. Milk = $36$ litres. Let $x$ litres of water be added. Total mixture = $40 + x$, New water = $4 + x$. $\frac{4 + x}{40 + x} = \frac{20}{100} = \frac{1}{5}$ $5(4 + x) = 40 + x \implies 20 + 5x = 40 + x$ $4x = 20 \implies x = 5$ litres.

Question 5

5. If the price of sugar is increased by $20\%$, by what percentage must a housewife reduce her consumption so that the expenditure on sugar remains the same?

A) $20\%$

B) $16\frac{2}{3}\%$

C) $25\%$

D) $15\%$

Answer

Correct Answer: B

Reduction in consumption = $(\frac{r}{100 + r}) \times 100\%$ Here $r = 20$. Reduction = $(\frac{20}{120}) \times 100 = \frac{1}{6} \times 100 = 16.66\% = 16\frac{2}{3}\%$.

Question 6

6. In an election between two candidates, one got $55\%$ of the total valid votes, and $20\%$ of the votes were invalid. If the total number of votes was $7500$, the number of valid votes that the other candidate got, was:

A) $3100$

B) $2900$

C) $2700$

D) $3000$

Answer

Correct Answer: C

Total votes = $7500$. Invalid votes = $20\% \text{ of } 7500 = 1500$. Valid votes = $7500 - 1500 = 6000$. Candidate A got $55\%$ of valid votes. Candidate B got $100\% - 55\% = 45\%$ of valid votes. Valid votes for B = $45\% \text{ of } 6000 = 0.45 \times 6000 = 2700$.

Question 7

7. 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) $40$ kg

B) $32$ kg

C) $52$ kg

D) $80$ kg

Answer

Correct Answer: A

The quantity of pulp remains constant. Pulp in fresh fruit = $100 - 68 = 32\%$. Pulp in dry fruit = $100 - 20 = 80\%$. Let $x$ be the weight of dry fruit. $80\% \text{ of } x = 32\% \text{ of } 100$ $0.8x = 32 \implies x = \frac{32}{0.8} = 40$ kg.

Question 8

8. A's salary is $25\%$ more than B's salary. B's salary is $20\%$ less than C's salary. If C's salary is $₹ 20,000$, find A's salary.

A) $₹ 18,000$

B) $₹ 22,000$

C) $₹ 25,000$

D) $₹ 20,000$

Answer

Correct Answer: D

C's salary = $20,000$. B's salary = $20,000 - 20\% \text{ of } 20,000 = 20,000 - 4,000 = 16,000$. A's salary = $16,000 + 25\% \text{ of } 16,000 = 16,000 + 4,000 = 20,000$. Thus, A's salary is same as C's.

Question 9

9. In an examination, $35\%$ of the candidates failed in Mathematics and $25\%$ in English. If $10\%$ failed in both Mathematics and English, then how much percent of candidates passed in both the subjects?

A) $40\%$

B) $50\%$

C) $60\%$

D) $30\%$

Answer

Correct Answer: B

Using Venn Diagram formula: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$. Failed in at least one subject = $35\% + 25\% - 10\% = 50\%$. Passed in both subjects = $100\% - 50\% = 50\%$.

Question 10

10. The price of an item is decreased by $25\%$. In order to restore its original price, the new price must be increased by:

A) $25\%$

B) $20\%$

C) $33\frac{1}{3}\%$

D) $40\%$

Answer

Correct Answer: C

Let original price be $100$. Decreased price = $100 - 25 = 75$. To restore to $100$, increase needed = $100 - 75 = 25$. Percentage increase on new price = $(\frac{25}{75}) \times 100 = \frac{1}{3} \times 100 = 33\frac{1}{3}\%$.

Competitive Exams : Quantitative Aptitude - Percentage (Set 1) | Concept of Maths