Question 1

A town's population decreased by 10% from 2019 to 2020. If the population in 2020 was 360,000, what was the population in 2019?

Accepted Answer

Step 1: Let population in 2019 = P. Step 2: After 10% decrease, population in 2020 = P × (1 - 0.10) = 0.90P. Step 3: 0.90P = 360,000. Step 4: P = 360,000 ÷ 0.90 = 400,000.

Question 2

The population of a town decreased from 50,000 to 40,000. What is the percentage decrease in population?

Accepted Answer

Step 1: Calculate the decrease = 50,000 - 40,000 = 10,000. Step 2: Apply percentage formula: (Decrease / Original Population) × 100 = (10,000 / 50,000) × 100 = 20%. Therefore, the percentage decrease is 20%.

Question 3

In an examination, 65% of students passed in Mathematics and 75% passed in English. If 55% passed in both subjects, what percentage of students failed in both subjects?

Accepted Answer

Step 1: Let total students = 100. Step 2: Students who passed in at least one subject = (Passed in Math) + (Passed in English) - (Passed in both) = 65 + 75 - 55 = 85. Step 3: Students who failed in both subjects = 100 - 85 = 15%.

Question 4

The population of a city was 500,000 in 2020. If it increases by 20% in 2021, what will be the population in 2021?

Accepted Answer

Step 1: Initial population = 500,000. Step 2: Increase = 20% of 500,000 = 0.20 × 500,000 = 100,000. Step 3: Population in 2021 = 500,000 + 100,000 = 600,000.

Question 5

If a district's population is 600,000 and 35% are children, how many children are there in the district?

Accepted Answer

Step 1: Total population = 600,000. Step 2: Percentage of children = 35%. Step 3: Number of children = 35% of 600,000 = 0.35 × 600,000 = 210,000.

Question 6

A shopkeeper bought a shirt for ₹400. He marked it up by 50% and then gave a discount of 20% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Step 2: Marked Price (MP) = 400 + 50% of 400 = 400 + 200 = ₹600. Step 3: Discount = 20% of 600 = ₹120. Step 4: Selling Price (SP) = 600 - 120 = ₹480. Step 5: Profit = 480 - 400 = ₹80. Step 6: Profit % = (80/400) × 100 = 20%.

Question 7

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

Accepted Answer

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

Question 8

A shopkeeper reduced the price of a book 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 9

A mobile phone's price is reduced by 30%. If the new price is ₹14,000, what was the original price?

Accepted Answer

Step 1: Let original price = x. Step 2: After 30% reduction, new price = x - 30% of x = 0.70x. Step 3: 0.70x = 14,000. Step 4: x = 14,000 ÷ 0.70 = ₹20,000.

Question 10

The price of sugar increased by 25%. By what percentage should a family reduce its consumption to keep the expenditure the same?

Accepted Answer

Step 1: Let original price = P and original consumption = C. Original expenditure = P × C. Step 2: New price = 1.25P. Step 3: For same expenditure: 1.25P × New Consumption = P × C. Step 4: New Consumption = C ÷ 1.25 = 0.80C. Step 5: Reduction in consumption = C - 0.80C = 0.20C. Step 6: Percentage reduction = (0.20C ÷ C) × 100 = 20%.

Question 11

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

Question 12

A student scored 72% in an exam and obtained 360 marks. What are the total marks of the exam?

Accepted Answer

Step 1: Let total marks = x. Step 2: 72% of x = 360. Step 3: 0.72x = 360. Step 4: x = 360 ÷ 0.72 = 500.

Question 13

The population of a village increased from 80,000 to 96,000 over two years. What is the percentage increase?

Accepted Answer

Step 1: Initial population = 80,000. Step 2: Final population = 96,000. Step 3: Increase = 96,000 - 80,000 = 16,000. Step 4: Percentage increase = (16,000 ÷ 80,000) × 100 = 0.20 × 100 = 20%.

Question 14

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

Accepted Answer

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

Question 15

A company's revenue increased from ₹2,00,000 to ₹2,50,000. What is the percentage increase in revenue?

Accepted Answer

Step 1: Calculate the increase = 2,50,000 - 2,00,000 = ₹50,000. Step 2: Apply percentage formula: (Increase / Original Revenue) × 100 = (50,000 / 2,00,000) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 16

The number of employees in a factory decreased from 1,200 to 1,000. What is the percentage decrease in the number of employees?

Accepted Answer

Step 1: Calculate the decrease = 1,200 - 1,000 = 200. Step 2: Apply percentage formula: (Decrease / Original Number) × 100 = (200 / 1,200) × 100 = 16.67%. Rounding to nearest whole number gives approximately 16.67% or 50/3 %. However, exact calculation: (200/1200) × 100 = 16⅔%. Therefore, the percentage decrease is 16⅔% or 16.67%.

Question 17

A state's population was 2,000,000 in 2015. By 2025, it became 2,640,000. What is the percentage increase over this 10-year period?

Accepted Answer

Step 1: Initial population (2015) = 2,000,000. Step 2: Final population (2025) = 2,640,000. Step 3: Increase = 2,640,000 - 2,000,000 = 640,000. Step 4: Percentage increase = (640,000 ÷ 2,000,000) × 100 = 0.32 × 100 = 32%.

Question 18

A company's revenue increased from ₹50 lakhs to ₹65 lakhs. What is the percentage increase in revenue?

Accepted Answer

Step 1: Original revenue = ₹50 lakhs. New revenue = ₹65 lakhs. Step 2: Increase = 65 - 50 = ₹15 lakhs. Step 3: Percentage increase = (Increase ÷ Original) × 100 = (15 ÷ 50) × 100 = 30%.

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

Question 20

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.

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