Question 1

If 45% of a number is 360, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: 45% of x = 360, so 0.45x = 360. Step 3: x = 360 ÷ 0.45 = 800. Therefore, the number is 800.

Question 2

A shopkeeper marks an item at ₹500. He offers a 20% discount. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 20% of 500 = 0.20 × 500 = ₹100. Step 3: Selling Price = MP − Discount = 500 − 100 = ₹400. Therefore, the selling price is ₹400.

Question 3

In an exam, 65% of students passed. If 390 students passed, how many students appeared in total?

Accepted Answer

Step 1: Let total students = x. Step 2: 65% of x = 390, so 0.65x = 390. Step 3: x = 390 ÷ 0.65 = 600. Therefore, 600 students appeared in total.

Question 4

A number is increased by 25%. If the new number is 500, what was the original number?

Accepted Answer

Step 1: Let original number = x. Step 2: After 25% increase, new number = x + 0.25x = 1.25x. Step 3: 1.25x = 500, so x = 500 ÷ 1.25 = 400. Therefore, the original number was 400.

Question 5

What is 18% of 250?

Accepted Answer

Step 1: 18% of 250 = (18/100) × 250. Step 2: = 0.18 × 250 = 45. Therefore, 18% of 250 is 45.

Question 6

If a price increases from ₹200 to ₹250, what is the percentage increase?

Accepted Answer

Step 1: Increase in price = ₹250 − ₹200 = ₹50. Step 2: Percentage increase = (Increase / Original Price) × 100 = (50 / 200) × 100. Step 3: = 0.25 × 100 = 25%. Therefore, the percentage increase is 25%.

Question 7

In a city, 45% of the population is male and 55% is female. If 30% of males and 20% of females are unemployed, what percentage of the total population is unemployed?

Accepted Answer

Step 1: Let total population = 100 (for easy calculation). Step 2: Males = 45, Females = 55. Step 3: Unemployed males = 30% of 45 = 0.30 × 45 = 13.5. Step 4: Unemployed females = 20% of 55 = 0.20 × 55 = 11. Step 5: Total unemployed = 13.5 + 11 = 24.5. Step 6: Percentage of total population unemployed = 24.5%. Therefore, the answer is 24.5%.

Question 8

The population of a district increases by 25% in the first year and then by 20% in the second year. If the population after two years is 1,50,000, what was the original population?

Accepted Answer

Step 1: Let the original population be P. Step 2: After first year: P × 1.25. Step 3: After second year: P × 1.25 × 1.20 = P × 1.50. Step 4: P × 1.50 = 1,50,000. Step 5: P = 1,50,000 ÷ 1.50 = 1,00,000. Therefore, the answer is 1,00,000.

Question 9

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 10

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 in 2022?

Accepted Answer

Step 1: Population in 2021 = 500,000 + (20% of 500,000) = 500,000 + 100,000 = 600,000. Step 2: Population in 2022 = 600,000 − (10% of 600,000) = 600,000 − 60,000 = 540,000. Therefore, the answer is 540,000.

Question 11

In a town, the male population is 60% of the total. If the female population is 48,000, what is the total population of the town?

Accepted Answer

Step 1: If males are 60%, then females are 40% of the total. Step 2: Let total population = P. Then 40% of P = 48,000. Step 3: 0.40 × P = 48,000. Step 4: P = 48,000 ÷ 0.40 = 120,000. Therefore, the answer is 120,000.

Question 12

A town's population was 2,50,000 in 2019. In 2020, it decreased by 8%, and in 2021, it increased by 10%. In 2022, it decreased by 5%. What is the population in 2022?

Accepted Answer

Step 1: Population in 2020 = 2,50,000 × 0.92 = 2,30,000. Step 2: Population in 2021 = 2,30,000 × 1.10 = 2,53,000. Step 3: Population in 2022 = 2,53,000 × 0.95 = 2,40,350. Therefore, the answer is 2,40,350.

Question 13

In an examination, 35% of students failed in Mathematics, 25% failed in English, and 10% failed in both subjects. What percentage of students passed in both subjects?

Accepted Answer

Step 1: Let total students = 100. Failed in Math = 35, Failed in English = 25, Failed in both = 10. Step 2: Failed in at least one subject = 35 + 25 - 10 = 50 (using inclusion-exclusion principle). Step 3: Passed in both = 100 - 50 = 50%.

Question 14

A number is increased by 25%, and then the result is decreased by 20%. What is the net change in the number as a percentage?

Accepted Answer

Step 1: Let the original number = 100. Step 2: After 25% increase = 100 + 25 = 125. Step 3: After 20% decrease on 125 = 125 - (20% of 125) = 125 - 25 = 100. Step 4: Net change = 100 - 100 = 0. Net change percentage = 0%.

Question 15

A student scored 45% in an exam and failed by 30 marks. If he had scored 55%, he would have passed by 10 marks. What is the passing percentage?

Accepted Answer

Step 1: Let total marks = x. At 45%, score = 0.45x, and he failed by 30 marks, so passing marks = 0.45x + 30. Step 2: At 55%, score = 0.55x, and he passed by 10 marks, so passing marks = 0.55x - 10. Step 3: Equate: 0.45x + 30 = 0.55x - 10. Step 4: 40 = 0.10x, so x = 400. Step 5: Passing marks = 0.45(400) + 30 = 180 + 30 = 210. Step 6: Passing percentage = (210/400) × 100 = 52.5%.

Question 16

The price of a commodity increases by 15% in the first year and decreases by 10% in the second year. If the price at the end of the second year is ₹2,070, what was the original price?

Accepted Answer

Step 1: Let original price = P. After 15% increase in year 1 = P × 1.15. Step 2: After 10% decrease in year 2 = P × 1.15 × 0.90 = P × 1.035. Step 3: P × 1.035 = 2,070. Step 4: P = 2,070 / 1.035 = 2,000.

Question 17

A person spends 30% of his income on rent, 25% on food, and 15% on transport. If he saves ₹1,800 per month, which is the remaining percentage of his income, what is his total monthly income?

Accepted Answer

Step 1: Total spent = 30% + 25% + 15% = 70%. Step 2: Remaining (savings) = 100% - 70% = 30%. Step 3: 30% of income = ₹1,800. Step 4: Income = 1,800 / 0.30 = ₹6,000.

Question 18

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price. If the cost price of an item is ₹400, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Step 2: Marked Price (MP) = 400 + 60% of 400 = 400 + 240 = ₹640. Step 3: Discount = 25% of 640 = 160. Step 4: Selling Price (SP) = 640 - 160 = ₹480. Step 5: Profit = 480 - 400 = ₹80. Step 6: Profit % = (80/400) × 100 = 20%.

Question 19

A number is increased by 20%, then the result is decreased by 20%. What is the net change in the original number as a percentage?

Accepted Answer

Step 1: Let the original number be x. Step 2: After 20% increase: x × 1.20 = 1.2x. Step 3: After 20% decrease on the new value: 1.2x × 0.80 = 0.96x. Step 4: Net change = 0.96x - x = -0.04x. Step 5: Percentage change = (-0.04x/x) × 100 = -4%.

Question 20

In an election, candidate A received 45% of votes, candidate B received 35% of votes, and the remaining votes were invalid. If the total number of valid votes was 8000, how many invalid votes were cast?

Accepted Answer

Step 1: Valid votes = 8000. Step 2: A's votes = 45% of total votes, B's votes = 35% of total votes. Step 3: Valid votes percentage = 45% + 35% = 80% of total votes. Step 4: Invalid votes percentage = 100% - 80% = 20% of total votes. Step 5: If 80% of total = 8000, then total votes = 8000/0.80 = 10,000. Step 6: Invalid votes = 20% of 10,000 = 2,000.

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