Question 1

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 2

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 3

The population of a city increases by 20% in the first year and by 25% in the second year. If the population at the end of the second year is 3,60,000, what was the population at the beginning of the first year?

Accepted Answer

Step 1: Let the initial population be P. After first year, population = P × 1.20. Step 2: After second year, population = P × 1.20 × 1.25 = P × 1.50. Step 3: We know P × 1.50 = 3,60,000. Step 4: Therefore, P = 3,60,000 ÷ 1.50 = 2,40,000.

Question 4

The population of a city increases by 20% in the first year and decreases by 10% in the second year. If the population after two years is 2,16,000, what was the initial population of the city?

Accepted Answer

Step 1: Let the initial population be P. After first year (20% increase): P × 1.20 = 1.20P. Step 2: After second year (10% decrease): 1.20P × 0.90 = 1.08P. Step 3: We know 1.08P = 2,16,000. Step 4: Therefore, P = 2,16,000 ÷ 1.08 = 2,00,000. Step 5: Verification: 2,00,000 × 1.20 = 2,40,000 (after year 1); 2,40,000 × 0.90 = 2,16,000 (after year 2) ✓

Question 5

The population of a city was 5,00,000 in 2020. It increased by 20% in 2021 and then decreased by 10% in 2022. In 2023, it increased by 15%. What is the population of the city at the end of 2023?

Accepted Answer

Step 1: Population after 2021 = 5,00,000 × (1 + 20/100) = 5,00,000 × 1.20 = 6,00,000. Step 2: Population after 2022 = 6,00,000 × (1 - 10/100) = 6,00,000 × 0.90 = 5,40,000. Step 3: Population after 2023 = 5,40,000 × (1 + 15/100) = 5,40,000 × 1.15 = 6,21,000. Therefore, the population at the end of 2023 is 6,21,000.

Question 6

The population of a city increases by 20% in the first year and by 25% in the second year. However, due to migration, the population decreases by 10% in the third year. If the population at the end of the third year is 16,20,000, what was the original population at the beginning of the first year?

Accepted Answer

Step 1: Let the original population be P. After year 1: P × 1.20. After year 2: P × 1.20 × 1.25 = P × 1.50. After year 3: P × 1.50 × 0.90 = P × 1.35. Step 2: We know P × 1.35 = 16,20,000. Step 3: P = 16,20,000 ÷ 1.35 = 12,00,000. Therefore, the original population was 12,00,000.

Question 7

The population of a city increases by 20% in the first year and by 25% in the second year. However, due to migration, the population decreases by 10% in the third year. If the population after three years is 16,20,000, what was the original population?

Accepted Answer

Step 1: Let the original population be P. After year 1: P × 1.20. After year 2: P × 1.20 × 1.25 = P × 1.50. After year 3: P × 1.50 × 0.90 = P × 1.35. Step 2: We know P × 1.35 = 16,20,000. Step 3: P = 16,20,000 ÷ 1.35 = 12,00,000.

Question 8

A district's population was 400,000 in 2019. In 2020, it increased by 10%, and in 2021, it decreased by 10%. What is the population in 2021?

Accepted Answer

Step 1: Population in 2020 = 400,000 × 1.10 = 440,000. Step 2: Population in 2021 = 440,000 × 0.90 = 396,000. Step 3: Final population = 396,000.

Question 9

A city's population was 250,000 in 2019. It increased by 10% in 2020 and then increased by 20% in 2021. What was the population at the end of 2021?

Accepted Answer

Step 1: Population in 2019 = 250,000. Step 2: After 10% increase in 2020 = 250,000 × 1.10 = 275,000. Step 3: After 20% increase in 2021 = 275,000 × 1.20 = 330,000.

Question 10

A town's population decreased by 15% over one year. If the population at the end of the year was 170,000, what was the population at the beginning of the year?

Accepted Answer

Step 1: Let initial population = P. Step 2: After 15% decrease, population = P × (1 - 0.15) = 0.85P. Step 3: 0.85P = 170,000. Step 4: P = 170,000 ÷ 0.85 = 200,000.

Question 11

A state's population increases by 25% to reach 1,250,000. What was the original population?

Accepted Answer

Step 1: Let original population = P. Step 2: After 25% increase: P + 0.25P = 1.25P = 1,250,000. Step 3: P = 1,250,000 / 1.25 = 1,000,000.

Question 12

The population of village A is 80,000 and the population of village B is 120,000. By what percentage is village B's population more than village A's population?

Accepted Answer

Step 1: Difference = 120,000 - 80,000 = 40,000. Step 2: Percentage more = (Difference ÷ Village A's population) × 100. Step 3: Percentage = (40,000 ÷ 80,000) × 100 = 0.5 × 100 = 50%.

Question 13

If a population increases from 250,000 to 300,000, what is the percentage increase?

Accepted Answer

Step 1: Increase = 300,000 - 250,000 = 50,000. Step 2: Percentage increase = (Increase ÷ Original) × 100 = (50,000 ÷ 250,000) × 100 = 0.20 × 100 = 20%.

Question 14

In a city, 45% of the population are males and the rest are females. If there are 220,000 females, how many males are there in the city?

Accepted Answer

Step 1: If 45% are males, then females = 100% - 45% = 55%. Step 2: Let total population = P. Then 0.55P = 220,000. Step 3: P = 220,000 ÷ 0.55 = 400,000. Step 4: Males = 45% of 400,000 = 0.45 × 400,000 = 180,000.

Question 15

A village population increased from 80,000 to 96,000 over two years. What was the percentage increase in population?

Accepted Answer

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

Question 16

A village had a population of 80,000 in 2020. The population decreased by 15% in 2021. What was the population in 2021?

Accepted Answer

Step 1: Initial population = 80,000. Step 2: Decrease = 15% of 80,000 = 0.15 × 80,000 = 12,000. Step 3: Population in 2021 = 80,000 - 12,000 = 68,000.

Question 17

A town's population decreased by 10% in one year. If the population at the end of the year was 360,000, what was the population at the beginning of the year?

Accepted Answer

Step 1: Let initial population = P. Step 2: After 10% decrease, population = P × (1 - 10/100) = 0.90P. Step 3: Given 0.90P = 360,000. Step 4: P = 360,000 ÷ 0.90 = 400,000.

Question 18

The population of town A is 250,000 and the population of town B is 200,000. By what percentage is town A's population more than town B's population?

Accepted Answer

Step 1: Difference = 250,000 - 200,000 = 50,000. Step 2: Percentage more = (Difference / Town B population) × 100 = (50,000 / 200,000) × 100 = 25%.

Question 19

The population of a city was 500,000 in 2020. If it 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 20

If a region's population was 600,000 last year and it is now 660,000, what is the percentage increase?

Accepted Answer

Step 1: Last year's population = 600,000, Current population = 660,000. Step 2: Increase = 660,000 - 600,000 = 60,000. Step 3: Percentage increase = (60,000 / 600,000) × 100 = 10%.

Question 21

A city's population grows from 400,000 to 480,000 over one year. What is the percentage growth rate?

Accepted Answer

Step 1: Initial population = 400,000, Final population = 480,000. Step 2: Growth = 480,000 - 400,000 = 80,000. Step 3: Growth percentage = (80,000 / 400,000) × 100 = 20%.

Question 22

A city's population grows by 25% in the first year and then by 20% in the second year. If the initial population was 100,000, what is the population after two years?

Accepted Answer

Step 1: After year 1: 100,000 × 1.25 = 125,000. Step 2: After year 2: 125,000 × 1.20 = 150,000. Step 3: Final population = 150,000.

Question 23

The population of a city is 500,000. If it increases by 20% in the first year, what will be the population after the first year?

Accepted Answer

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

Question 24

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: Population at end of 2021 = 500,000 + 100,000 = 600,000.

Question 25

The population of a city was 500,000 in 2020. If it 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 26

In a town, the male population is 55% of the total population. If the female population is 180,000, what is the total population of the town?

Accepted Answer

Step 1: If males are 55%, then females are 100% - 55% = 45% of the total population. Step 2: Let total population = P. Then 0.45P = 180,000. Step 3: P = 180,000 ÷ 0.45 = 400,000. Therefore, the total population is 400,000.

Question 27

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.

KVS PGT Population Problems

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Population Problems — Practice Questions

60-Second Revision — Population Problems