Question 1

The price of a commodity increased by 20% last year and decreased by 10% this year. What is the net change in price over the two years?

Accepted Answer

Step 1: Let original price = 100. Step 2: After 20% increase: Price = 100 + 20 = 120. Step 3: After 10% decrease on 120: Price = 120 - (10% of 120) = 120 - 12 = 108. Step 4: Net change = 108 - 100 = 8. Step 5: Net change percentage = (8/100) × 100 = 8%.

Question 2

The population of a town increased from 200,000 to 240,000 over one year. What was the percentage increase in population?

Accepted Answer

Step 1: Initial population = 200,000, Final population = 240,000. Step 2: Increase = 240,000 - 200,000 = 40,000. Step 3: Percentage increase = (Increase / Original) × 100 = (40,000 / 200,000) × 100 = 0.20 × 100 = 20%.

Question 3

A shopkeeper marks his goods at 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 4

A student scored 72% in English and 68% in Mathematics. If English carries 80 marks and Mathematics carries 100 marks, what is the overall percentage scored by the student?

Accepted Answer

Step 1: Marks in English = 72% of 80 = 0.72 × 80 = 57.6. Step 2: Marks in Mathematics = 68% of 100 = 0.68 × 100 = 68. Step 3: Total marks obtained = 57.6 + 68 = 125.6. Step 4: Total marks = 80 + 100 = 180. Step 5: Overall percentage = (125.6/180) × 100 = 69.78% ≈ 70%.

Question 5

A person's salary is increased by 15%. If his new salary is ₹46,000, what was his original salary?

Accepted Answer

Step 1: Let original salary = S. New salary = S + 15% of S = 1.15S. Step 2: 1.15S = 46,000. Step 3: S = 46,000 / 1.15 = 40,000.

Question 6

A village had a population of 80,000 in 2019. The population decreased by 15% in 2020. What was the population at the end of 2020?

Accepted Answer

Step 1: Initial population = 80,000. Step 2: Decrease = 15% of 80,000 = 0.15 × 80,000 = 12,000. Step 3: Final population = 80,000 - 12,000 = 68,000.

Question 7

A shopkeeper reduced the price of an item by 25%. The reduced price is ₹450. What was the original price?

Accepted Answer

Step 1: Let original price = P. Step 2: After 25% reduction, new price = P - 0.25P = 0.75P. Step 3: 0.75P = 450. Step 4: P = 450 ÷ 0.75 = ₹600.

Question 8

The population of a town decreased from 80,000 to 72,000. What is the percentage decrease?

Accepted Answer

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

Question 9

A shopkeeper buys an item for ₹200 and sells it at a profit of 35%. What is the selling price?

Accepted Answer

Step 1: Cost price = ₹200. Step 2: Profit = 35% of 200 = (35/100) × 200 = ₹70. Step 3: Selling price = Cost price + Profit = 200 + 70 = ₹270. Therefore, the selling price is ₹270.

Question 10

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: Votes for A = 55% of 8000 = 0.55 × 8000 = 4400. Step 2: Votes for B = 45% of 8000 = 0.45 × 8000 = 3600. Step 3: Difference = 4400 - 3600 = 800.

Question 11

What is 25% of 480?

Accepted Answer

Step 1: Use the percentage formula: Percentage of a number = (Percentage/100) × Number. Step 2: 25% of 480 = (25/100) × 480 = 0.25 × 480 = 120. Therefore, the answer is 120.

Question 12

A mobile phone is sold for ₹18,000 after giving a discount of 25%. What was the marked price of the mobile phone?

Accepted Answer

Step 1: Let marked price = MP. Discount = 25%, so selling price = 75% of MP. Step 2: 75% of MP = 18,000. Step 3: MP = 18,000 / 0.75 = 24,000.

Question 13

If 15% of a number is 45, what is the number?

Accepted Answer

Step 1: Let the number be x. Then 15% of x = 45. Step 2: (15/100) × x = 45. Step 3: 0.15x = 45. Step 4: x = 45 ÷ 0.15 = 300. Therefore, the number is 300.

Question 14

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

Accepted Answer

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

Question 15

A shirt costs ₹800. Its price is increased by 20%. What is the new price?

Accepted Answer

Step 1: Original price = ₹800. Step 2: Increase = 20% of 800 = (20/100) × 800 = ₹160. Step 3: New price = Original price + Increase = 800 + 160 = ₹960. Therefore, the new price is ₹960.

Question 16

In an exam, a student scored 72 marks out of 120. What is the percentage of marks obtained?

Accepted Answer

Step 1: Marks obtained = 72, Total marks = 120. Step 2: Percentage = (Marks obtained / Total marks) × 100. Step 3: Percentage = (72/120) × 100 = 0.6 × 100 = 60%. Therefore, the percentage is 60%.

Question 17

A book's price is reduced by 30%. If the original price was ₹500, what is the sale price?

Accepted Answer

Step 1: Original price = ₹500. Step 2: Reduction = 30% of 500 = (30/100) × 500 = ₹150. Step 3: Sale price = Original price − Reduction = 500 − 150 = ₹350. Therefore, the sale price is ₹350.

Question 18

A student's marks increased from 60 to 75. What is the percentage increase in marks?

Accepted Answer

Step 1: Increase in marks = 75 - 60 = 15. Step 2: Percentage increase = (Increase ÷ Original) × 100. Step 3: Percentage increase = (15 ÷ 60) × 100 = 25%.

Question 19

The price of a shirt was increased by 20%. If the new price is ₹600, what was the original price?

Accepted Answer

Step 1: Let original price = x. Step 2: After 20% increase, new price = x + 0.20x = 1.20x. Step 3: 1.20x = 600. Step 4: x = 600 ÷ 1.20 = ₹500.

Question 20

A city's population was 150,000 in 2018. It increased by 10% in 2019 and then by 20% in 2020. What was the population at the end of 2020?

Accepted Answer

Step 1: Population in 2018 = 150,000. Step 2: After 10% increase in 2019 = 150,000 × 1.10 = 165,000. Step 3: After 20% increase in 2020 = 165,000 × 1.20 = 198,000.

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