Question 1

In an examination, 35% of students failed in Mathematics and 28% failed in English. If 10% failed in both subjects, what percentage of students passed in both subjects?

Accepted Answer

Step 1: Students who failed in at least one subject = Failed in Maths + Failed in English - Failed in both = 35% + 28% - 10% = 53%. Step 2: Students who passed in both subjects = 100% - 53% = 47%.

Question 2

A village population decreased from 80,000 to 72,000 over one year. What was the percentage decrease?

Accepted Answer

Step 1: Original population = 80,000. Step 2: New population = 72,000. Step 3: Decrease = 80,000 - 72,000 = 8,000. Step 4: Percentage decrease = (8,000 / 80,000) × 100 = 10%.

Question 3

If a town's population increases by 25% to reach 50,000, what was the original population?

Accepted Answer

Step 1: Let original population = P. Step 2: After 25% increase, population = P + 0.25P = 1.25P. Step 3: 1.25P = 50,000. Step 4: P = 50,000 / 1.25 = 40,000.

Question 4

A district's population was 200,000 in 2019. It increased by 15% in 2020 and then decreased by 10% in 2021. What was the population in 2021?

Accepted Answer

Step 1: Population in 2020 = 200,000 × 1.15 = 230,000. Step 2: Population in 2021 = 230,000 × 0.90 = 207,000.

Question 5

A city's population is 400,000. If 35% are children, 45% are adults, and the rest are elderly, how many elderly people are there?

Accepted Answer

Step 1: Total population = 400,000. Step 2: Children = 35%, Adults = 45%. Step 3: Elderly percentage = 100% - 35% - 45% = 20%. Step 4: Elderly population = 20% of 400,000 = 0.20 × 400,000 = 80,000.

Question 6

A number is increased by 20% and then decreased by 20%. What is the net change in the number?

Accepted Answer

Step 1: Let the original number = 100. After 20% increase = 100 + 20 = 120. Step 2: After 20% decrease on 120 = 120 - (20% of 120) = 120 - 24 = 96. Step 3: Net change = 96 - 100 = -4. Net change percentage = (-4/100) × 100 = -4% (or 4% decrease).

Question 7

A student scored 65% in one exam and 75% in another exam. If the first exam has a weightage of 40% and the second exam has a weightage of 60%, what is the weighted average score?

Accepted Answer

Step 1: Weighted average = (Score₁ × Weight₁) + (Score₂ × Weight₂) = (65 × 0.40) + (75 × 0.60). Step 2: = 26 + 45 = 71%.

Question 8

The price of an item was reduced by 25%. By what percentage should the reduced price be increased to restore it to the original price?

Accepted Answer

Step 1: Let original price = 100. Reduced price = 100 - 25 = 75. Step 2: To restore to 100, increase needed = 100 - 75 = 25. Step 3: Percentage increase = (25/75) × 100 = 33.33% (or 33⅓%).

Question 9

A company's revenue increased from ₹50 lakhs to ₹65 lakhs. What is the percentage increase in revenue?

Accepted Answer

Step 1: Increase in revenue = 65 - 50 = 15 lakhs. Step 2: Percentage increase = (Increase / Original) × 100 = (15 / 50) × 100 = 30%.

Question 10

The population of two cities A and B are in the ratio 3:5. If city A has 90,000 people, how many people does city B have?

Accepted Answer

Step 1: Ratio A:B = 3:5. Step 2: If A = 90,000, then 3 units = 90,000. Step 3: 1 unit = 30,000. Step 4: B = 5 units = 5 × 30,000 = 150,000.

Question 11

A shopkeeper marks his goods 40% above the cost price. If he gives a discount of 10% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let cost price = 100. Marked price = 100 + 40% of 100 = 140. Step 2: Discount = 10% of 140 = 14. Selling price = 140 - 14 = 126. Step 3: Profit = 126 - 100 = 26. Profit percentage = (26/100) × 100 = 26%.

Question 12

The population of a city was 500,000 in 2020. If it increased by 20% in 2021, what was the population in 2021?

Accepted Answer

Step 1: Initial population = 500,000. Step 2: Increase = 20% of 500,000 = 0.20 × 500,000 = 100,000. Step 3: Population in 2021 = 500,000 + 100,000 = 600,000.

Question 13

In a school, 60% of students are boys. If there are 240 boys, what is the total number of students in the school?

Accepted Answer

Step 1: Let total students = x. Boys = 60% of x = 0.60x. Step 2: 0.60x = 240. Step 3: x = 240 ÷ 0.60 = 400 students.

Question 14

The price of a commodity increased by 25% in the first year and then decreased by 20% in the second year. If the original price was ₹400, what is the final price after two years?

Accepted Answer

Step 1: Price after first year = 400 + 25% of 400 = 400 × 1.25 = ₹500. Step 2: Price after second year = 500 - 20% of 500 = 500 × 0.80 = ₹400. Step 3: Final price = ₹400.

Question 15

A shopkeeper marks his goods 40% above the cost price. If he gives a discount of 20% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let cost price = ₹100. Marked price = 100 + 40% of 100 = ₹140. Step 2: Discount = 20% of 140 = ₹28. Selling price = 140 - 28 = ₹112. Step 3: Profit = 112 - 100 = ₹12. Profit percentage = (12/100) × 100 = 12%.

Question 16

In an election, candidate A received 55% of the votes and candidate B received the remaining votes. If the total number of votes cast was 8000, how many more votes did A receive than B?

Accepted Answer

Step 1: Candidate A received 55% of 8000 = 0.55 × 8000 = 4400 votes. Step 2: Candidate B received remaining votes = 8000 - 4400 = 3600 votes. Step 3: Difference = 4400 - 3600 = 800 votes.

Question 17

The population of a city was 500,000 in 2020. It increased by 20% in 2021 and then decreased by 10% in 2022. What is the population at the end of 2022?

Accepted Answer

Step 1: Population after 20% increase in 2021 = 500,000 × 1.20 = 600,000. Step 2: Population after 10% decrease in 2022 = 600,000 × 0.90 = 540,000. Therefore, the population at the end of 2022 is 540,000.

Question 18

A town's population in 2019 was 80,000. If the population increased by 15% each year for 2 years, what is the population in 2021?

Accepted Answer

Step 1: Population after 1st year (2020) = 80,000 × 1.15 = 92,000. Step 2: Population after 2nd year (2021) = 92,000 × 1.15 = 105,800. Therefore, the population in 2021 is 105,800.

Question 19

In a village, 45% of the population are males and the rest are females. If there are 22,000 females, what is the total population of the village?

Accepted Answer

Step 1: If 45% are males, then females = 100% - 45% = 55%. Step 2: Let total population = P. Then 55% of P = 22,000. Step 3: 0.55 × P = 22,000. Step 4: P = 22,000 ÷ 0.55 = 40,000. Therefore, the total population is 40,000.

Question 20

The population of two towns A and B are in the ratio 3:5. If town A's population increased by 20% and town B's population increased by 10%, what is the new ratio of their populations?

Accepted Answer

Step 1: Let initial populations be 3x and 5x respectively. Step 2: After increase, town A's population = 3x × 1.20 = 3.6x. Step 3: After increase, town B's population = 5x × 1.10 = 5.5x. Step 4: New ratio = 3.6x : 5.5x = 3.6 : 5.5 = 36 : 55. Therefore, the new ratio is 36:55.

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