Question 1

A district's population is currently 2,00,000. If it grows at 8% per year, what will the population be after one year?

Accepted Answer

Step 1: Current population = 2,00,000. Step 2: Growth = 8% of 2,00,000 = 0.08 × 2,00,000 = 16,000. Step 3: Population after 1 year = 2,00,000 + 16,000 = 2,16,000.

Question 2

A shopkeeper sells a shirt for ₹480, which is 20% more than its cost price. What is the cost price of the shirt?

Accepted Answer

Step 1: Let cost price = CP. Selling price = 480. Step 2: SP = CP + 20% of CP = 1.2 × CP. Step 3: 1.2 × CP = 480. Step 4: CP = 480 ÷ 1.2 = 400. Therefore, cost price is ₹400.

Question 3

In an exam, 35% of students failed. If 260 students passed, how many students appeared for the exam?

Accepted Answer

Step 1: If 35% failed, then 65% passed. Step 2: 65% of total = 260. Step 3: 0.65 × Total = 260. Step 4: Total = 260 ÷ 0.65 = 400. Therefore, 400 students appeared for the exam.

Question 4

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

Accepted Answer

Step 1: Original price = ₹200, New price = ₹250. Step 2: Increase = 250 - 200 = ₹50. Step 3: Percentage increase = (Increase ÷ Original) × 100 = (50 ÷ 200) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 5

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

Accepted Answer

Step 1: Marks obtained = 360, Percentage = 72%. Step 2: 72% of Total marks = 360. Step 3: 0.72 × Total = 360. Step 4: Total = 360 ÷ 0.72 = 500. Therefore, total marks = 500.

Question 6

A factory produced 5,000 units last month. This month, production increased by 12%. How many units were produced this month?

Accepted Answer

Step 1: Last month's production = 5,000 units. Step 2: Increase = 12% of 5,000 = 0.12 × 5,000 = 600 units. Step 3: This month's production = 5,000 + 600 = 5,600 units. Therefore, 5,600 units were produced this month.

Question 7

The population of a city is 50,000. If it increases by 20% in the first year, what will be the population after one year?

Accepted Answer

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

Question 8

A town's population was 80,000 last year. This year it decreased by 15%. What is the current population?

Accepted Answer

Step 1: Last year's population = 80,000. Step 2: Decrease = 15% of 80,000 = 0.15 × 80,000 = 12,000. Step 3: Current population = 80,000 - 12,000 = 68,000.

Question 9

If a village population increases from 25,000 to 30,000, what is the percentage increase?

Accepted Answer

Step 1: Initial population = 25,000, Final population = 30,000. Step 2: Increase = 30,000 - 25,000 = 5,000. Step 3: Percentage increase = (Increase / Initial) × 100 = (5,000 / 25,000) × 100 = 20%.

Question 10

A city's population was 1,20,000 two years ago. It increased by 10% in the first year and then by 5% in the second year. What is the population now?

Accepted Answer

Step 1: Initial population = 1,20,000. Step 2: After 1st year = 1,20,000 + 10% of 1,20,000 = 1,20,000 + 12,000 = 1,32,000. Step 3: After 2nd year = 1,32,000 + 5% of 1,32,000 = 1,32,000 + 6,600 = 1,38,600.

Question 11

The population of a region decreased from 90,000 to 72,000. What is the percentage decrease?

Accepted Answer

Step 1: Initial population = 90,000, Final population = 72,000. Step 2: Decrease = 90,000 - 72,000 = 18,000. Step 3: Percentage decrease = (Decrease / Initial) × 100 = (18,000 / 90,000) × 100 = 20%.

Question 12

A company's revenue was ₹50 lakhs last year. This year it increased to ₹65 lakhs. Next year, the revenue is projected to decrease by 10% from this year's figure. What will be the revenue next year?

Accepted Answer

Step 1: This year's revenue = ₹65 lakhs. Step 2: Next year's revenue = 65 - (10% of 65) = 65 - 6.5 = ₹58.5 lakhs. Step 3: Alternatively, next year's revenue = 65 × 0.90 = ₹58.5 lakhs.

Question 13

A shopkeeper marks his goods 40% above the cost price. If he gives a discount of 20% 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 = 20% of 140 = 28. Selling price = 140 - 28 = 112. Step 3: Profit = 112 - 100 = 12. Profit percentage = (12/100) × 100 = 12%.

Question 14

In an examination, 35% of students failed in Hindi, 28% failed in English, and 20% failed in both subjects. What percentage of students passed in both subjects?

Accepted Answer

Step 1: Let total students = 100. Failed in Hindi = 35, Failed in English = 28, Failed in both = 20. Step 2: Using set theory: Failed in at least one subject = 35 + 28 - 20 = 43. Step 3: Passed in both subjects = 100 - 43 = 57%.

Question 15

A person spends 30% of his income on rent, 25% on food, and 15% on transport. The remaining amount is ₹1,800. What is his total monthly income?

Accepted Answer

Step 1: Total percentage spent = 30% + 25% + 15% = 70%. Step 2: Remaining percentage = 100% - 70% = 30%. Step 3: If 30% = ₹1,800, then 100% = (1,800 ÷ 30) × 100 = 60 × 100 = ₹6,000.

Question 16

The population of a city was 500,000 in 2020. It increased by 20% in 2021 and then decreased by 10% in 2022. What is the population at the end of 2022?

Accepted Answer

Step 1: Population after 20% increase in 2021 = 500,000 × 1.20 = 600,000. Step 2: Population after 10% decrease in 2022 = 600,000 × 0.90 = 540,000. Therefore, the population at the end of 2022 is 540,000.

Question 17

A village's population was 80,000 in 2019. The population increased by 15% in 2020 and by 25% in 2021. What was the percentage increase in population from 2019 to 2021?

Accepted Answer

Step 1: Population after 2020 = 80,000 × 1.15 = 92,000. Step 2: Population after 2021 = 92,000 × 1.25 = 115,000. Step 3: Total increase = 115,000 - 80,000 = 35,000. Step 4: Percentage increase = (35,000 / 80,000) × 100 = 43.75%. Therefore, the percentage increase is 43.75%.

Question 18

The population of town A is 240,000 and the population of town B is 360,000. If town A's population increases by 30% and town B's population decreases by 20%, what will be the ratio of their populations after these changes?

Accepted Answer

Step 1: Town A's new population = 240,000 × 1.30 = 312,000. Step 2: Town B's new population = 360,000 × 0.80 = 288,000. Step 3: Ratio = 312,000 : 288,000. Step 4: Simplify by dividing both by 24,000: 13 : 12. Therefore, the ratio is 13:12.

Question 19

In a district, the male population is 55% of the total population. If the total population is 500,000, and the male population increases by 10% while the female population decreases by 5%, what will be the new total population?

Accepted Answer

Step 1: Male population = 55% of 500,000 = 275,000. Step 2: Female population = 45% of 500,000 = 225,000. Step 3: New male population = 275,000 × 1.10 = 302,500. Step 4: New female population = 225,000 × 0.95 = 213,750. Step 5: New total population = 302,500 + 213,750 = 516,250. Therefore, the new total population is 516,250.

Question 20

The population of a region was 800,000 in 2015. By 2020, it had increased to 1,000,000. What was the percentage increase in population over this 5-year period?

Accepted Answer

Step 1: Increase in population = 1,000,000 - 800,000 = 200,000. Step 2: Percentage increase = (200,000 / 800,000) × 100 = 25%. Therefore, the percentage increase is 25%.

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