Question 1

A city's population was 400,000 in 2015. If the population increased to 480,000 by 2018, what was the percentage increase?

Accepted Answer

Step 1: Initial population = 400,000. Step 2: Final population = 480,000. Step 3: Increase = 480,000 − 400,000 = 80,000. Step 4: Percentage increase = (80,000 / 400,000) × 100 = 20%.

Question 2

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 3

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 4

The population of a town was 250,000 in 2018. It increased by 10% in 2019 and then increased by 20% in 2020. What was the population at the end of 2020?

Accepted Answer

Step 1: Population 2018 = 250,000. Step 2: After 10% increase in 2019 = 250,000 × 1.10 = 275,000. Step 3: After 20% increase in 2020 = 275,000 × 1.20 = 330,000.

Question 5

The population of a district decreased from 600,000 to 510,000 over 5 years. What was the percentage decrease?

Accepted Answer

Step 1: Initial population = 600,000. Step 2: Final population = 510,000. Step 3: Decrease = 600,000 − 510,000 = 90,000. Step 4: Percentage decrease = (90,000 / 600,000) × 100 = 15%.

Question 6

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) × 100 = (200 / 800) × 100 = 25%. Therefore, the percentage decrease is 25%.

Question 7

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 8

The price of a commodity increased by 20% and then decreased by 20%. What is the net change in price?

Accepted Answer

Step 1: Let original price = 100. Step 2: After 20% increase: 100 + 20 = 120. Step 3: After 20% decrease on 120: 120 - (20% of 120) = 120 - 24 = 96. Step 4: Net change = 96 - 100 = -4. Net change percentage = (-4/100) × 100 = -4% (a decrease of 4%).

Question 9

A person spends 35% of his income on rent, 25% on food, and 20% on utilities. If he saves ₹8000, what is his total monthly income?

Accepted Answer

Step 1: Total spending percentage = 35% + 25% + 20% = 80%. Step 2: Savings percentage = 100% - 80% = 20%. Step 3: If 20% of income = 8000, then income = 8000 ÷ 0.20 = 40,000.

Question 10

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: (Obtained / Total) × 100. Step 2: Substitute values: (72 / 120) × 100 = 0.6 × 100 = 60%. Therefore, the percentage of marks obtained is 60%.

Question 11

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

Accepted Answer

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

Question 12

The cost of a laptop was ₹40,000. After a discount, it was sold for ₹32,000. What is the percentage discount offered?

Accepted Answer

Step 1: Calculate the discount amount = 40,000 − 32,000 = ₹8,000. Step 2: Apply percentage discount formula: (Discount / Original Price) × 100 = (8,000 / 40,000) × 100 = 20%. Therefore, the percentage discount offered is 20%.

Question 13

In a town, 45% of the population is male. If the total population is 200,000, how many females are there?

Accepted Answer

Step 1: Total population = 200,000. Step 2: Male percentage = 45%. Step 3: Female percentage = 100% − 45% = 55%. Step 4: Number of females = 55% of 200,000 = 0.55 × 200,000 = 110,000.

Question 14

The price of a mobile phone increased from ₹15,000 to ₹18,000. What is the percentage increase in price?

Accepted Answer

Step 1: Calculate the increase in price = 18,000 − 15,000 = ₹3,000. Step 2: Apply percentage change formula: (Change / Original) × 100 = (3,000 / 15,000) × 100 = 20%. Therefore, the percentage increase is 20%.

Question 15

A student scored 72% in an exam and obtained 360 marks. What was the maximum marks for the exam?

Accepted Answer

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

Question 16

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 17

A company's revenue decreased from ₹5,00,000 to ₹4,00,000. What is the percentage decrease in revenue?

Accepted Answer

Step 1: Calculate the decrease in revenue = 5,00,000 − 4,00,000 = ₹1,00,000. Step 2: Apply percentage decrease formula: (Decrease / Original Revenue) × 100 = (1,00,000 / 5,00,000) × 100 = 20%. Therefore, the percentage decrease in revenue is 20%.

Question 18

A student scored 60% marks in an exam. If the total marks were increased from 100 to 150, and the student's marks are adjusted proportionally, what percentage of marks does the student now have?

Accepted Answer

Step 1: Student scored 60% of 100 = 60 marks. Step 2: When total marks increase to 150, the student's marks are adjusted proportionally: New marks = 60 × (150/100) = 60 × 1.5 = 90. Step 3: Percentage in new system = (90/150) × 100 = 60%. Therefore, the percentage remains 60%.

Question 19

The population of a city was 500,000 in 2020. It increased by 10% in 2021 and by 15% in 2022. What was the population in 2022?

Accepted Answer

Step 1: Population in 2020 = 500,000. Step 2: After 10% increase in 2021: Population = 500,000 × 1.10 = 550,000. Step 3: After 15% increase in 2022: Population = 550,000 × 1.15 = 632,500. Therefore, population in 2022 was 632,500.

Question 20

In a state, the population increased by 15% from 2010 to 2015, and then decreased by 10% from 2015 to 2020. If the population in 2020 was 20,70,000, what was the population in 2010?

Accepted Answer

Step 1: Let population in 2010 = P. After 15% increase: P × 1.15. After 10% decrease: P × 1.15 × 0.90 = P × 1.035. Step 2: P × 1.035 = 20,70,000. Step 3: P = 20,70,000 ÷ 1.035 = 20,00,000.

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