Question 1

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 2

A merchant bought goods for ₹8,000. He wants to make a profit of 25%. At what price should he sell the goods?

Accepted Answer

Step 1: Cost price = ₹8,000. Required profit percentage = 25%. Step 2: Profit = 25% of 8,000 = (25/100) × 8,000 = ₹2,000. Step 3: Selling price = Cost price + Profit = 8,000 + 2,000 = ₹10,000.

Question 3

A worker's salary increased from ₹18,000 to ₹22,500. What is the percentage increase in salary?

Accepted Answer

Step 1: Calculate the increase in salary = 22,500 - 18,000 = ₹4,500. Step 2: Apply percentage increase formula: (Increase / Original Salary) × 100 = (4,500 / 18,000) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 4

The value of a car depreciates from ₹8,00,000 to ₹6,40,000. What is the percentage depreciation?

Accepted Answer

Step 1: Calculate the depreciation amount = 8,00,000 - 6,40,000 = ₹1,60,000. Step 2: Apply percentage depreciation formula: (Depreciation / Original Value) × 100 = (1,60,000 / 8,00,000) × 100 = 20%. Therefore, the percentage depreciation is 20%.

Question 5

The price of a commodity increased by 20% in the first year and decreased by 25% in the second year. What is the net change in price over two years?

Accepted Answer

Step 1: Let original price = 100. After 20% increase: Price = 100 + 20 = 120. Step 2: After 25% decrease on 120: Price = 120 - (25% of 120) = 120 - 30 = 90. Step 3: Net change = 90 - 100 = -10. Net change percentage = (-10/100) × 100 = -10% (decrease).

Question 6

A town's population was 50,000 in 2020. It increased by 10% in 2021 and by 20% in 2022. What was the population in 2022?

Accepted Answer

Step 1: Population in 2020 = 50,000. Population in 2021 = 50,000 + 10% of 50,000 = 50,000 + 5,000 = 55,000. Step 2: Population in 2022 = 55,000 + 20% of 55,000 = 55,000 + 11,000 = 66,000.

Question 7

A student scored 45 marks out of 60 in an exam. In the next exam, the student scores 54 marks out of 60. What is the percentage increase in marks?

Accepted Answer

Step 1: Calculate the increase in marks = 54 - 45 = 9 marks. Step 2: Apply percentage increase formula: (Increase / Original Marks) × 100 = (9 / 45) × 100 = 20%. Therefore, the percentage increase is 20%.

Question 8

The population of a town decreases from 80,000 to 60,000. What is the percentage decrease?

Accepted Answer

Step 1: Calculate the decrease = 80,000 - 60,000 = 20,000. Step 2: Apply percentage decrease formula: (Decrease / Original) × 100 = (20,000 / 80,000) × 100 = 25%. Therefore, the percentage decrease is 25%.

Question 9

The price of a commodity was ₹250. After a discount, it becomes ₹200. What is the percentage discount?

Accepted Answer

Step 1: Calculate the discount amount = 250 - 200 = ₹50. Step 2: Apply percentage discount formula: (Discount / Original Price) × 100 = (50 / 250) × 100 = 20%. Therefore, the percentage discount is 20%.

Question 10

The population of a town was 50,000 in 2020. If it increased by 20% in 2021, what was the population at the end of 2021?

Accepted Answer

Step 1: Initial population = 50,000. Step 2: Increase = 20% of 50,000 = 0.20 × 50,000 = 10,000. Step 3: Population at end of 2021 = 50,000 + 10,000 = 60,000.

Question 11

A shopkeeper marks a shirt at ₹800. He gives a discount of 20%. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹800, Discount = 20%. Step 2: Discount amount = 20% of 800 = (20/100) × 800 = ₹160. Step 3: Selling Price (SP) = MP − Discount = 800 − 160 = ₹640. Therefore, the selling price is ₹640.

Question 12

In an examination, 65% of students passed in English and 75% passed in Mathematics. If 15% failed in both subjects, what percentage of students passed in both subjects?

Accepted Answer

Step 1: Students who failed in English = 100 - 65 = 35%. Students who failed in Mathematics = 100 - 75 = 25%. Step 2: Using the principle: Failed in at least one subject = Failed in English + Failed in Math - Failed in both = 35 + 25 - 15 = 45%. Step 3: Passed in both = 100 - 45 = 55%.

Question 13

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

Accepted Answer

Step 1: Use the percentage formula: Percentage = (Obtained Marks / Total Marks) × 100. Step 2: Percentage = (72/120) × 100. Step 3: Simplify: (72/120) = (3/5) = 0.6. Step 4: 0.6 × 100 = 60%. Therefore, the percentage is 60%.

Question 14

A student scored 45% marks in an examination and failed by 36 marks. If passing marks are 55%, how many total marks were there in the examination?

Accepted Answer

Step 1: Let total marks = x. Marks scored = 45% of x = 0.45x. Passing marks = 55% of x = 0.55x. Step 2: The student failed by 36 marks, so: 0.55x - 0.45x = 36. Step 3: 0.10x = 36, therefore x = 360.

Question 15

The price of a book increased from ₹200 to ₹250. What is the percentage increase?

Accepted Answer

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

Question 16

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 17

A student's test score improved from 60% to 75%. What is the percentage point increase in the score?

Accepted Answer

Step 1: Initial Score = 60%, Final Score = 75%. Step 2: Percentage Point Increase = Final Score − Initial Score = 75% − 60% = 15 percentage points. Note: This is NOT the same as a 25% relative increase. Therefore, the percentage point increase is 15 percentage points.

Question 18

A shopkeeper increases the price of a shirt from ₹400 to ₹500. What is the percentage increase in price?

Accepted Answer

Step 1: Calculate the increase in price = 500 - 400 = ₹100. Step 2: Apply percentage change formula: (Change / Original) × 100 = (100 / 400) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 19

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 20

The population of village A is 30,000 and the population of village B is 45,000. By what percentage is village B's population more than village A's?

Accepted Answer

Step 1: Difference = 45,000 - 30,000 = 15,000. Step 2: Percentage more = (Difference ÷ Village A's population) × 100. Step 3: Percentage = (15,000 ÷ 30,000) × 100 = 0.5 × 100 = 50%.

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