Question 1

A student scored 450 marks out of 600 in an examination. What percentage of marks did the student score?

Accepted Answer

Step 1: Use the formula: Percentage = (Marks Obtained / Total Marks) × 100. Step 2: Percentage = (450 / 600) × 100 = 0.75 × 100 = 75%. Therefore, the student scored 75%.

Question 2

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 12% of ₹500 = (12/100) × 500 = ₹60. Step 3: Selling Price (SP) = MP − Discount = 500 − 60 = ₹440. Therefore, the selling price is ₹440.

Question 3

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 4

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: x = 45 × (100/15) = 45 × (20/3) = 300. Therefore, the number is 300.

Question 5

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 6

The population of a city was 5,00,000 in 2020. It increased by 20% in 2021 and then decreased by 10% in 2022. What is the population of the city at the end of 2022?

Accepted Answer

Step 1: Population in 2021 = 5,00,000 + 20% of 5,00,000 = 5,00,000 + 1,00,000 = 6,00,000. Step 2: Population in 2022 = 6,00,000 − 10% of 6,00,000 = 6,00,000 − 60,000 = 5,40,000. Therefore, the population at the end of 2022 is 5,40,000.

Question 7

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

Accepted Answer

Step 1: Use the formula Percentage = (Obtained/Total) × 100. Step 2: Percentage = (72/120) × 100. Step 3: Simplify: (72/120) = (3/5) = 0.60. Step 4: 0.60 × 100 = 60%. Therefore, the percentage score is 60%.

Question 8

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 9

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 10

If 45% of a number is 360, what is 20% of that number?

Accepted Answer

Step 1: Let the number be x. Then 45% of x = 360, so 0.45x = 360. Step 2: Solve for x: x = 360 ÷ 0.45 = 800. Step 3: Find 20% of 800: 0.20 × 800 = 160. Therefore, the answer is 160.

Question 11

The population of a city was 500,000 in 2020. If the population increased by 20% in 2021 and then decreased by 10% in 2022, what was the population at the end of 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 population at the end of 2022 was 540,000.

Question 12

In a class of 200 students, 45% are boys. How many girls are there?

Accepted Answer

Step 1: Total students = 200. Boys = 45% of 200 = (45/100) × 200 = 90. Step 2: Girls = Total - Boys = 200 - 90 = 110. Therefore, there are 110 girls.

Question 13

A shopkeeper marks up the price of an item by 40% above its cost price. If he then offers a discount of 20% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let cost price (CP) = ₹100. Step 2: Marked price (MP) = 100 + 40% of 100 = ₹140. Step 3: Discount = 20% of 140 = ₹28. Step 4: Selling price (SP) = 140 − 28 = ₹112. Step 5: Profit = SP − CP = 112 − 100 = ₹12. Step 6: Profit % = (12/100) × 100 = 12%. Therefore, the answer is 12%.

Question 14

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 = 800 + 160 = ₹960. Therefore, the new price is ₹960.

Question 15

In an examination, a student scored 72% and obtained 360 marks. What is the total marks of the examination?

Accepted Answer

Step 1: Let total marks = x. Step 2: 72% of x = 360, so 0.72x = 360. Step 3: Solve for x: x = 360 ÷ 0.72 = 500. Therefore, the total marks is 500.

Question 16

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 17

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 18

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 19

The price of a commodity increased by 25%. If the new price is ₹750, what was the original price?

Accepted Answer

Step 1: Let the original price = x. Step 2: After 25% increase, new price = x + 0.25x = 1.25x. Step 3: Given that 1.25x = 750, so x = 750 ÷ 1.25 = 600. Therefore, the original price was ₹600.

Question 20

What is 25% of 480?

Accepted Answer

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

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