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: Option C

Explanation: Let Initial Income = 100. Expenditure = 75, Savings = 100 - 75 = 25. New Income = 100 + 20% of 100 = 120. New Expenditure = 75 + 10% 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 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) 500B) 600C) 800D) 1000

Answer

✓ Correct Answer: Option A

Explanation: 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 litresB) 10 litresC) 8 litresD) 5 litres

Answer

✓ Correct Answer: Option D

Explanation: Initial water = 10% 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 ⇒ 20 + 5x = 40 + x 4x = 20 ⇒ 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: Option B

Explanation: 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) 3100B) 2900C) 2700D) 3000

Answer

✓ Correct Answer: Option C

Explanation: Total votes = 7500. Invalid votes = 20% 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 = $45% of 6000 = 0.45 \times 6000 = 2700$.

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 kgB) 32 kgC) 52 kgD) 80 kg

Answer

✓ Correct Answer: Option A

Explanation: 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% of x = 32% of 100 $0.8x = 32 ⇒ x = \frac{32}{0.8} = 40$ 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) ₹18,000B) ₹22,000C) ₹25,000D) ₹20,000

Answer

✓ Correct Answer: Option D

Explanation: C's salary = 20,000. B's salary = 20,000 - 20% of 20,000 = 20,000 - 4,000 = 16,000. A's salary = 16,000 + 25% 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: Option B

Explanation: 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: Option C

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

Accepted Answer

✓ Correct Answer: Option B

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

Competitive Exams : Quantitative Aptitude - Percentage (Set 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.

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?

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:

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?

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?

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:

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?

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.

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?

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