Question 1

A district's population was 5,00,000 in 2015. If the population increased by 8% per year for 2 years, what was the population in 2017?

Accepted Answer

Step 1: Initial population (2015) = 5,00,000. Step 2: After 1 year (2016) = 5,00,000 × 1.08 = 5,40,000. Step 3: After 2 years (2017) = 5,40,000 × 1.08 = 5,83,200.

Question 2

The population of a town was 50,000 in 2020. If it increased by 20% in 2021, what was the population at the end of 2021?

Accepted Answer

Step 1: Initial population = 50,000. Step 2: Increase = 20% of 50,000 = 0.20 × 50,000 = 10,000. Step 3: Population at end of 2021 = 50,000 + 10,000 = 60,000.

Question 3

The population of village A is 30,000 and the population of village B is 45,000. By what percentage is village B's population more than village A's?

Accepted Answer

Step 1: Difference = 45,000 - 30,000 = 15,000. Step 2: Percentage more = (Difference ÷ Village A's population) × 100. Step 3: Percentage = (15,000 ÷ 30,000) × 100 = 0.5 × 100 = 50%.

Question 4

A town's population in 2019 was 80,000. It increased by 10% in 2020 and then by 20% in 2021. What was the population at the end of 2021?

Accepted Answer

Step 1: Population in 2019 = 80,000. Step 2: After 10% increase in 2020 = 80,000 × 1.10 = 88,000. Step 3: After 20% increase in 2021 = 88,000 × 1.20 = 105,600.

Question 5

If a region's population increases from 2,00,000 to 2,40,000, what is the percentage increase?

Accepted Answer

Step 1: Initial population = 2,00,000. Step 2: Final population = 2,40,000. Step 3: Increase = 2,40,000 - 2,00,000 = 40,000. Step 4: Percentage increase = (40,000 ÷ 2,00,000) × 100 = 20%.

Question 6

The population of a town is 80,000. It increases by 10% in the first year and decreases by 10% in the second year. What is the population of the town at the end of two years?

Accepted Answer

Step 1: Population after first year (10% increase) = 80,000 × 1.10 = 88,000. Step 2: Population after second year (10% decrease) = 88,000 × 0.90 = 79,200. Therefore, the population at the end of two years is 79,200. Shortcut: Net % change = +10 - 10 - (10×10)/100 = -1%, so final population = 80,000 × 0.99 = 79,200.

Question 7

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 8

In a town, the male population is 45% of the total. If the female population is 66,000, what is the total population of the town?

Accepted Answer

Step 1: If males are 45%, then females are 100% - 45% = 55% of the total. Step 2: Let total population = P. Then 55% of P = 66,000. Step 3: 0.55P = 66,000, so P = 66,000 ÷ 0.55 = 120,000. Therefore, the total population is 120,000.

Question 9

In a city, 35% of the population is below 18 years old. If 42,000 people are below 18 years old, how many people are 18 years or older?

Accepted Answer

Step 1: Let total population = P. Then 35% of P = 42,000. Step 2: 0.35P = 42,000, so P = 42,000 ÷ 0.35 = 1,20,000. Step 3: Population 18 years or older = 100% - 35% = 65% of total. Step 4: 65% of 1,20,000 = 0.65 × 1,20,000 = 78,000. Therefore, 78,000 people are 18 years or older.

Question 10

The population of a city increases by 20% in the first year and by 25% in the second year. If the population after two years is 3,60,000, what was the original population?

Accepted Answer

Step 1: Let original population = P. After year 1: P × 1.20. After year 2: P × 1.20 × 1.25 = P × 1.50. Step 2: P × 1.50 = 3,60,000. Step 3: P = 3,60,000 ÷ 1.50 = 2,40,000.

Question 11

A town's population was 5,00,000 in 2010. It decreased by 10% in 2011 and then increased by 20% in 2012. In 2013, it decreased by 5%. What is the population in 2013?

Accepted Answer

Step 1: 2010 population = 5,00,000. Step 2: After 2011 (−10%): 5,00,000 × 0.90 = 4,50,000. Step 3: After 2012 (+20%): 4,50,000 × 1.20 = 5,40,000. Step 4: After 2013 (−5%): 5,40,000 × 0.95 = 5,13,000.

Question 12

A district's population in 2015 was 8,00,000. The population growth rate was 5% per year for the first two years and 8% per year for the next two years. What was the population in 2019?

Accepted Answer

Step 1: 2015 population = 8,00,000. Step 2: After 2016 and 2017 (5% each year): 8,00,000 × 1.05 × 1.05 = 8,00,000 × 1.1025 = 8,82,000. Step 3: After 2018 and 2019 (8% each year): 8,82,000 × 1.08 × 1.08 = 8,82,000 × 1.1664 = 10,28,109 ≈ 10,28,109.

Question 13

A city's population consists of 45% males and 55% females. The male population increases by 18% while the female population decreases by 10%. If the original population was 10,00,000, what is the new total population?

Accepted Answer

Step 1: Original population = 10,00,000. Males = 45% × 10,00,000 = 4,50,000. Females = 55% × 10,00,000 = 5,50,000. Step 2: New males = 4,50,000 × 1.18 = 5,31,000. Step 3: New females = 5,50,000 × 0.90 = 4,95,000. Step 4: New total = 5,31,000 + 4,95,000 = 10,26,000.

Question 14

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 15

The population of a district increased by 25% in the first year and then decreased by 20% in the second year. If the initial population was 200,000, what is the population after two years?

Accepted Answer

Step 1: Initial population = 200,000. Step 2: After 25% increase in year 1: 200,000 × 1.25 = 250,000. Step 3: After 20% decrease in year 2: 250,000 × 0.80 = 200,000.

Question 16

In a city, the male population is 60% of the total population. If the male population is 360,000, what is the total population of the city?

Accepted Answer

Step 1: Let total population = T. Step 2: Male population = 60% of T = 0.60T. Step 3: 0.60T = 360,000. Step 4: T = 360,000 ÷ 0.60 = 600,000.

Question 17

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 18

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: Given 0.85P = 170,000. Step 4: P = 170,000 ÷ 0.85 = 200,000.

Question 19

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

Accepted Answer

Step 1: Females = 55% of total population (since males are 45%). Step 2: 0.55 × Total = 220,000. Step 3: Total = 220,000 ÷ 0.55 = 400,000. Step 4: Males = 45% of 400,000 = 0.45 × 400,000 = 180,000.

Question 20

A city's population in 2019 was 400,000. It increased by 10% in 2020 and then increased by 5% in 2021. What was the population at the end of 2021?

Accepted Answer

Step 1: Population in 2019 = 400,000. Step 2: After 10% increase in 2020 = 400,000 × 1.10 = 440,000. Step 3: After 5% increase in 2021 = 440,000 × 1.05 = 462,000.

Question 21

A village population grows from 80,000 to 96,000 in two years. What is the percentage increase in population?

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 22

In a town, the male population is 45% of the total population. If the female population is 1,10,000, what is the total population of the town?

Accepted Answer

Step 1: If males are 45% of total, then females are 100% − 45% = 55% of total. Step 2: Let total population = P. Then 55% of P = 1,10,000. Step 3: 0.55 × P = 1,10,000, so P = 1,10,000 ÷ 0.55 = 2,00,000. Therefore, total population is 2,00,000.

Question 23

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 24

In a town, the male population is 60% of the total. If the male population is 360,000, what is the female population?

Accepted Answer

Step 1: Let total population = P. Then 0.60P = 360,000. Step 2: P = 360,000 ÷ 0.60 = 600,000. Step 3: Female population = 600,000 − 360,000 = 240,000. Therefore, the female population is 240,000.

Question 25

A village population grows at 15% per annum. If the current population is 8,000, what will be the population after 2 years (assuming compound growth)?

Accepted Answer

Step 1: Use compound growth formula: Final Population = Initial Population × (1 + rate/100)^time. Step 2: Population after 2 years = 8,000 × (1.15)^2 = 8,000 × 1.3225 = 10,580. Therefore, the population after 2 years is 10,580.

Question 26

In a city, 45% of the population is male and 55% is female. If 20% of males and 30% of females are unemployed, what percentage of the total population is unemployed?

Accepted Answer

Step 1: Assume total population = 100. Males = 45, Females = 55. Step 2: Unemployed males = 20% of 45 = 0.20 × 45 = 9. Step 3: Unemployed females = 30% of 55 = 0.30 × 55 = 16.5. Step 4: Total unemployed = 9 + 16.5 = 25.5. Step 5: Percentage of total population unemployed = 25.5%. Therefore, 25.5% of the total population is unemployed.

Question 27

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 at the end of 2022?

Accepted Answer

Step 1: Population after 20% increase in 2021 = 5,00,000 × 1.20 = 6,00,000. Step 2: Population after 10% decrease in 2022 = 6,00,000 × 0.90 = 5,40,000. Therefore, the population at the end of 2022 is 5,40,000.

Question 28

In a city, the ratio of male to female population is 7:5. If the male population increases by 25% and the female population decreases by 20%, the new ratio becomes 7:4. What is the percentage change in the total population?

Accepted Answer

Step 1: Let male population = 7x, female population = 5x. Original total = 12x. Step 2: New males = 7x × 1.25 = 8.75x. New females = 5x × 0.80 = 4x. Step 3: New total = 8.75x + 4x = 12.75x. Step 4: Percentage change = [(12.75x - 12x) / 12x] × 100 = (0.75x / 12x) × 100 = 6.25%.

Question 29

In a district, the population of males is 40% more than females. If 15% of males and 25% of females migrate out, the new male population is 2,04,000. What is the new total population of the district?

Accepted Answer

Step 1: Let female population = F. Male population = 1.40F. Step 2: After migration: Males remaining = 1.40F × (1 - 0.15) = 1.40F × 0.85 = 1.19F = 2,04,000. Step 3: F = 2,04,000 ÷ 1.19 ≈ 1,71,429. Step 4: Females remaining = F × 0.75 = 1,71,429 × 0.75 ≈ 1,28,572. Step 5: New total population = 2,04,000 + 1,28,572 = 3,32,572 ≈ 3,32,000 (or exactly 3,32,571 if F = 1,71,428.57).

Question 30

In a city, the male population is 55% of the total. The female population increases by 30% while the male population decreases by 10%. After these changes, the female population becomes 48% of the new total. If the original total population was 5,00,000, what is the new total population?

Accepted Answer

Step 1: Original male = 55% × 5,00,000 = 2,75,000. Original female = 45% × 5,00,000 = 2,25,000. Step 2: New male = 2,75,000 × (1 − 0.10) = 2,47,500. New female = 2,25,000 × (1 + 0.30) = 2,92,500. Step 3: New total population = 2,47,500 + 2,92,500 = 5,40,000. Step 4: Verification: Female % = 2,92,500 ÷ 5,40,000 = 54.17% (approximately 54%).

Question 31

A region's population comprises three groups: A (40%), B (35%), and C (25%). Group A's population increases by 15%, Group B decreases by 20%, and Group C increases by 40%. If the original population was 8,00,000 and the new population of Group C is 2,80,000, what is the new total population?

Accepted Answer

Step 1: Original Group C = 25% × 8,00,000 = 2,00,000. Step 2: New Group C = 2,00,000 × 1.40 = 2,80,000. (Verification: matches given data.) Step 3: Original Group A = 40% × 8,00,000 = 3,20,000. New Group A = 3,20,000 × 1.15 = 3,68,000. Step 4: Original Group B = 35% × 8,00,000 = 2,80,000. New Group B = 2,80,000 × 0.80 = 2,24,000. Step 5: New total = 3,68,000 + 2,24,000 + 2,80,000 = 8,72,000.

Question 32

The population of a city was 5,00,000 in 2015. It increased by 20% in the next 4 years and then decreased by 10% in the following 2 years. What is the population in 2021?

Accepted Answer

Step 1: Population after 4 years (2019) = 5,00,000 × 1.20 = 6,00,000. Step 2: Population after further 2 years (2021) = 6,00,000 × 0.90 = 5,40,000. Therefore, the answer is 5,40,000.

Question 33

A town's population was P in 2010. It increased by 30% by 2015, then decreased by 15% by 2020. In 2025, it increased by 20%. If the population in 2025 is 13,26,000, what was the population in 2010?

Accepted Answer

Step 1: Let population in 2010 = P. Step 2: Population in 2015 = P × 1.30. Step 3: Population in 2020 = P × 1.30 × 0.85 = P × 1.105. Step 4: Population in 2025 = P × 1.105 × 1.20 = P × 1.326. Step 5: P × 1.326 = 13,26,000 → P = 13,26,000 ÷ 1.326 = 10,00,000.

RRB NTPC Population Problems

RRB NTPC Population Problems — Past Exam Questions

Population Problems— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Population Problems — Practice Questions

60-Second Revision — Population Problems