Question 1

The number of employees in a company increased from 400 to 500. What is the percentage increase in the number of employees?

Accepted Answer

Step 1: Calculate the increase = 500 - 400 = 100 employees. Step 2: Apply percentage formula: (Increase / Original Number) × 100 = (100 / 400) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 2

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

Accepted Answer

Step 1: Calculate the increase = 250 - 200 = ₹50. Step 2: Apply percentage formula: (Increase / Original Price) × 100 = (50 / 200) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 3

The population of a town increased from 50,000 to 60,000. What is the percentage increase in population?

Accepted Answer

Step 1: Calculate the increase = 60,000 - 50,000 = 10,000. Step 2: Apply percentage formula: (Increase / Original Population) × 100 = (10,000 / 50,000) × 100 = 20%. Therefore, the percentage increase is 20%.

Question 4

A mobile phone's price decreased from ₹15,000 to ₹12,000. What is the percentage decrease in price?

Accepted Answer

Step 1: Calculate the decrease = 15,000 - 12,000 = ₹3,000. Step 2: Apply percentage formula: (Decrease / Original Price) × 100 = (3,000 / 15,000) × 100 = 20%. Therefore, the percentage decrease is 20%.

Question 5

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

Accepted Answer

Step 1: Calculate the increase = 20% of 50,000 = (20/100) × 50,000 = 10,000. Step 2: New population = Original population + Increase = 50,000 + 10,000 = 60,000. Therefore, the population in 2021 was 60,000.

Question 6

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

Accepted Answer

Step 1: Calculate the increase = 75 - 60 = 15 marks. Step 2: Apply percentage formula: (Increase / Original Marks) × 100 = (15 / 60) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 7

A student scored 72 marks out of 120 in an exam. What is the percentage of marks obtained?

Accepted Answer

Step 1: Apply the percentage formula: (Marks Obtained / Total Marks) × 100 = (72 / 120) × 100. Step 2: Simplify: (72 / 120) = (3 / 5) = 0.6. Step 3: Convert to percentage: 0.6 × 100 = 60%. Therefore, the percentage of marks obtained is 60%.

Question 8

The price of a commodity increases by 25% in the first year. In the second year, the price decreases by 20% from the increased price. What is the net percentage change in the price over the two years?

Accepted Answer

Step 1: Let the initial price be ₹100. Step 2: After 25% increase in year 1, price = 100 + (25% of 100) = 100 + 25 = ₹125. Step 3: In year 2, price decreases by 20% from ₹125, so decrease = 20% of 125 = 0.20 × 125 = ₹25. Step 4: Price after year 2 = 125 - 25 = ₹100. Step 5: Net change = 100 - 100 = ₹0. Step 6: Net percentage change = (0/100) × 100 = 0%. Therefore, the answer is 0%.

Question 9

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease?

Accepted Answer

Step 1: Calculate the decrease = 800 - 600 = ₹200. Step 2: Apply percentage formula: (Decrease / Original Price) × 100 = (200 / 800) × 100 = 25%. Therefore, the percentage decrease is 25%.

Question 10

The price of a shirt increased from ₹400 to ₹500. What is the percentage increase in the price?

Accepted Answer

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

Question 11

A shopkeeper buys goods at ₹800 per unit. He marks up the price by 40% and then offers a discount of 15% on the marked price. What is the profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Marked Price (MP) = 800 + (40% of 800) = 800 + 320 = ₹1120. Step 2: Discount = 15% of 1120 = 168. Selling Price (SP) = 1120 - 168 = ₹952. Step 3: Profit = 952 - 800 = ₹152. Profit % = (152/800) × 100 = 19%.

Question 12

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

Accepted Answer

Step 1: Let initial price = 100. After 25% increase: Price = 100 + 25 = 125. Step 2: After 20% decrease on 125: Price = 125 - (20% of 125) = 125 - 25 = 100. Step 3: Net change = 100 - 100 = 0. Therefore, net percentage change = 0%.

Question 13

The price of a laptop was increased by 20% and then decreased by 15%. What is the net percentage change in the price of the laptop?

Accepted Answer

Step 1: Let the original price = 100. Step 2: After 20% increase, new price = 100 × 1.20 = 120. Step 3: After 15% decrease on 120, final price = 120 × 0.85 = 102. Step 4: Net change = 102 − 100 = 2 (increase). Step 5: Net percentage change = 2%. Shortcut: Net% = a + b + (ab/100) = 20 + (−15) + (20×(−15)/100) = 5 − 3 = 2%. Therefore, answer is 2% increase.

Question 14

The price of a commodity increases by 25% in the first year. In the second year, the new price decreases by 20%. If the final price is ₹600, what was the original price?

Accepted Answer

Step 1: Let the original price be P. After 25% increase in year 1, price becomes P × 1.25. Step 2: After 20% decrease in year 2, price becomes P × 1.25 × 0.80 = P × 1.00. Step 3: So P × 1.00 = 600, therefore P = 600. Step 4: Verify: 600 × 1.25 = 750 (after year 1), then 750 × 0.80 = 600 (after year 2). Therefore, the original price was ₹600.

Question 15

The price of a commodity increases by 25% in the first year. In the second year, it decreases by 20% of the new price. In the third year, it increases by 10% of the price at the end of the second year. If the final price is ₹1,980, what was the original price?

Accepted Answer

Step 1: Let original price = P. After year 1 (25% increase): P × 1.25. Step 2: After year 2 (20% decrease): P × 1.25 × 0.80 = P × 1.00. Step 3: After year 3 (10% increase): P × 1.00 × 1.10 = P × 1.10. Step 4: Given final price = ₹1,980, so P × 1.10 = 1,980. Step 5: P = 1,980 ÷ 1.10 = ₹1,800. Therefore, the original price was ₹1,800.

Question 16

The salary of an employee was ₹30,000 per month. It was increased by 15%. What is the new salary?

Accepted Answer

Step 1: Calculate the increase = 15% of 30,000 = (15/100) × 30,000 = 4,500. Step 2: New salary = Original salary + Increase = 30,000 + 4,500 = 34,500. Therefore, the new salary is ₹34,500.

Question 17

The price of a commodity increases by 25% in the first month and then decreases by 20% in the second month. What is the net percentage change in the price over the two months?

Accepted Answer

Step 1: Let the initial price be ₹100. Step 2: After 25% increase in first month, price = 100 + (25% of 100) = 100 + 25 = ₹125. Step 3: After 20% decrease in second month, price = 125 - (20% of 125) = 125 - 25 = ₹100. Step 4: Net change = 100 - 100 = 0. Therefore, the net percentage change is 0%.

Question 18

A student scored 72 marks out of 120 in an exam. What is the percentage of marks obtained?

Accepted Answer

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

Question 19

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease?

Accepted Answer

Step 1: Calculate the decrease = 800 - 600 = ₹200. Step 2: Apply percentage formula: (Decrease / Original Price) × 100 = (200 / 800) × 100 = 25%. Therefore, the percentage decrease is 25%.

Question 20

The population of a village decreased from 5000 to 4500. What is the percentage decrease in population?

Accepted Answer

Step 1: Calculate the decrease in population = 5000 - 4500 = 500. Step 2: Apply percentage decrease formula = (Decrease / Original Population) × 100 = (500 / 5000) × 100 = 10%. Therefore, the percentage decrease is 10%.

Question 21

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

Accepted Answer

Step 1: Calculate the increase in marks = 75 - 60 = 15. Step 2: Apply percentage increase formula = (Increase / Original Marks) × 100 = (15 / 60) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 22

If the population of a town was 50,000 and it increased by 20%, what is the new population?

Accepted Answer

Step 1: Calculate the increase = 20% of 50,000 = (20/100) × 50,000 = 10,000. Step 2: New population = Original + Increase = 50,000 + 10,000 = 60,000. Therefore, the new population is 60,000.

Question 23

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

Accepted Answer

Step 1: Calculate the increase = 250 - 200 = ₹50. Step 2: Apply percentage formula: (Increase / Original Price) × 100 = (50 / 200) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 24

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease in price?

Accepted Answer

Step 1: Calculate the decrease in price = 800 - 600 = ₹200. Step 2: Apply percentage decrease formula = (Decrease / Original Price) × 100 = (200 / 800) × 100 = 25%. Therefore, the percentage decrease is 25%.

Question 25

The price of petrol decreased from ₹100 per litre to ₹80 per litre. What is the percentage decrease?

Accepted Answer

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

Question 26

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Let cost price (CP) = 100. Marked price (MP) = 100 + 60% of 100 = 160. Step 2: Discount = 25% of 160 = 40. Selling price (SP) = 160 - 40 = 120. Step 3: Profit = SP - CP = 120 - 100 = 20. Step 4: Profit % = (20/100) × 100 = 20%.

Question 27

The population of a town increases by 10% in the first year. In the second year, it decreases by 5%. In the third year, it increases by 8%. What is the net percentage change in population after three years?

Accepted Answer

Step 1: Let initial population = 100. After year 1 (+10%): Population = 100 × 1.10 = 110. Step 2: After year 2 (-5%): Population = 110 × 0.95 = 104.5. Step 3: After year 3 (+8%): Population = 104.5 × 1.08 = 112.86. Step 4: Net change = 112.86 - 100 = 12.86. Net percentage change = 12.86%.

Question 28

A shopkeeper buys goods at ₹500 per unit. He marks up the price by 40% but then offers a discount of 10% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Step 2: Marked Price (MP) = 500 + 40% of 500 = 500 + 200 = ₹700. Step 3: Selling Price (SP) = 700 − 10% of 700 = 700 − 70 = ₹630. Step 4: Profit = SP − CP = 630 − 500 = ₹130. Step 5: Profit % = (130/500) × 100 = 26%.

Question 29

A student's marks increased from 45 to 54. Later, the marks were recalculated and decreased from 54 to 48. What is the net percentage change in marks from the original value of 45?

Accepted Answer

Step 1: Original marks = 45. Final marks = 48. Step 2: Change in marks = 48 - 45 = 3. Step 3: Percentage change = (3/45) × 100 = 6.67% (or 20/3 %). Step 4: Since final marks (48) > original marks (45), this is a net increase of 6.67%.

Question 30

The value of a car depreciates by 15% in the first year and 10% in the second year. If the initial value was ₹5,00,000, what is the value after two years?

Accepted Answer

Step 1: Initial value = ₹5,00,000. After 15% depreciation: Value = 5,00,000 × (1 - 0.15) = 5,00,000 × 0.85 = ₹4,25,000. Step 2: After 10% depreciation on ₹4,25,000: Value = 4,25,000 × 0.90 = ₹3,82,500. Therefore, final value = ₹3,82,500.

Question 31

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

Accepted Answer

Step 1: Let initial price = 100. After 25% increase: Price = 100 + 25 = 125. Step 2: After 20% decrease on 125: Decrease = 125 × 20/100 = 25, so new price = 125 - 25 = 100. Step 3: Net change = 100 - 100 = 0. Therefore, net percentage change = 0%.

Question 32

The value of a car depreciates by 20% in the first year and 15% in the second year. If the initial value was ₹5,00,000, what is the value after two years?

Accepted Answer

Step 1: Initial value = ₹5,00,000. After 20% depreciation in year 1: Value = 5,00,000 × (1 - 0.20) = 5,00,000 × 0.80 = ₹4,00,000. Step 2: After 15% depreciation in year 2: Value = 4,00,000 × (1 - 0.15) = 4,00,000 × 0.85 = ₹3,40,000. Therefore, final value = ₹3,40,000.

Question 33

A shopkeeper marks up goods by 40% above cost price. He then offers a discount of 25% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Let cost price (CP) = 100. Marked price (MP) = 100 + 40% of 100 = 140. Step 2: Discount = 25% of 140 = 35. Selling price (SP) = 140 - 35 = 105. Step 3: Profit = SP - CP = 105 - 100 = 5. Profit percentage = (5/100) × 100 = 5%.

Question 34

The price of a commodity increases by 25% in the first year. In the second year, it decreases by 20% of the new price. If the original price was ₹800, what is the percentage change in price over the two years?

Accepted Answer

Step 1: After 25% increase in year 1, price = 800 × 1.25 = ₹1000. Step 2: After 20% decrease in year 2, price = 1000 × 0.80 = ₹800. Step 3: Net change = 800 − 800 = ₹0. Step 4: Percentage change = (0 / 800) × 100 = 0%. Therefore, the answer is 0% (no change).

Question 35

A number is increased by 50% and then decreased by 50%. What is the net percentage change?

Accepted Answer

Step 1: Let the number be 100. After 50% increase: 100 + 50 = 150. Step 2: After 50% decrease on 150: 150 - (50% of 150) = 150 - 75 = 75. Step 3: Net change = 75 - 100 = -25. Net percentage change = (-25/100) × 100 = -25%. Therefore, net percentage change = 25% decrease.

CDS Percentage Change

CDS Percentage Change — Past Exam Questions

Percentage Change— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Percentage Change — Practice Questions

60-Second Revision — Percentage Change