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AFCAT Population Problems

Study Material — 7 PYQs (2018–2020) · Concept Notes · Shortcuts

AFCAT Population Problems is a frequently tested subtopic — 7 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2020
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Previous Year Questions

AFCAT Population Problems — Past Exam Questions

7 questions from actual AFCAT papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

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?

Exam Q 22019Previous Year Pattern

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?

Exam Q 32019Previous Year Pattern

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?

Exam Q 42018Previous Year Pattern

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?

Exam Q 52020Previous Year Pattern

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?

Exam Q 62020Previous Year Pattern

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?

Exam Q 72019Previous Year Pattern

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?

Concept Notes

Population Problems— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

Population problems follow the compound growth formula. If a population increases or decreases by a certain percentage each year, you apply that percentage repeatedly, not just once. This is different from simple interest — it's like compound interest

KEY RULES

Population grows or shrinks by a fixed percentage each year 2. The percentage applies to the NEW population each year, not the original 3. Use the compound formula, not simple addition/subtraction 4. Decrease and increase work the same way mathematically

2.Formula Block

Memorise — at least one formula appears in every paper
Final Population = Initial Population × (1 + r/100)^n
- r = rate of increase (use negative r for decrease)
- n = number of years
- If r = 5% increase, use (1 + 5/100) = 1.05
- If r = 10% decrease, use (1 - 10/100) = 0.90

Where:

3.Exam Patterns

What examiners ask — read before attempting PYQs
1

Find final population after n years

2

Find initial population (work backwards)

3

Find rate of growth

4

Find time period

5

Mixed increase and decrease over different years

4.Worked Example

Solve this step-by-step before moving on
1
Step 1

Population after Year 1 = 50,000 × (1 + 10/100) = 50,000 × 1.10 = 55,000

2
Step 2

Population after Year 2 = 55,000 × (1 + 20/100) = 55,000 × 1.20 = 66,000 Alternative Direct Method: = 50,000 × 1.10 × 1.20 = 50,000 × 1.32 = 66,000

5.Exam Traps

Common mistakes students make — avoid these

Students add percentages directly: 10% + 20% = 30%, then calculate 50,000 × 1.30 = 65,000. This is WRONG because the 20% applies to the increased population, not the original. Always multiply the factors for each year.

Key Points to Remember

  • Population problems use compound growth formula: Final = Initial × (1 + r/100)^n
  • Percentage always applies to the CURRENT population, not the original amount
  • For decrease, use (1 - r/100) in the formula instead of (1 + r/100)
  • Multiple years with different rates: multiply all factors together for direct calculation
  • Never add percentages directly; always use multiplication of decimal factors
  • If asked for initial population, rearrange formula: Initial = Final ÷ (1 + r/100)^n

Exam-Specific Tips

  • Population formula: Final = Initial × (1 + r/100)^n where r is annual rate and n is years
  • For 10% increase, multiply by 1.10; for 10% decrease, multiply by 0.90
  • If population increases by p% one year and q% next year, combined factor = (1 + p/100) × (1 + q/100)
  • Compound population growth applies the percentage to the NEW amount each year, not original
  • For population decrease problems, the formula remains the same but r is treated as negative
  • Quick check: 50,000 population growing at 10% annually for 2 years = 50,000 × 1.21 = 60,500
Practice MCQs

Population Problems — Practice Questions

41graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 41

All MCQs →
Practice 1easy

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?

Practice 2easy

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?

Practice 3easy

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?

Practice 4easy

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?

Practice 5easy

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?

Practice 6easy

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

Practice 7easy

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

Practice 8easy

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?

Practice 9easy

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?

Practice 10easy

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?

Practice 11easy

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

Practice 12easy

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

Practice 13easy

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?

Practice 14easy

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

Practice 15easy

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?

Practice 16easy

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

Practice 17easy

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?

Practice 18easy

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?

Practice 19medium

A district's population decreased by 15% in the first year and then increased by 20% in the second year. If the population at the end of the second year is 408,000, what was the initial population?

Practice 20medium

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?

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60-Second Revision — Population Problems

  • Formula: Final Population = Initial × (1 + r/100)^n — this is compound, not simple
  • Trap: Never add percentages from different years. Multiply the growth factors instead
  • Decrease: Use negative r or write (1 - r/100) — both methods give same answer
  • Multi-year: For different rates each year, write as Initial × (1.10) × (1.20) × (0.95) etc.
  • Reverse: If given final population, divide backwards: Initial = Final ÷ [(1 + r/100)^n]
  • Quick mental check: 10% increase twice ≈ 21% total (not 20%), because second 10% acts on larger base
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