Study Material — 5 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC CPO Population Problems is a frequently tested subtopic — 5 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
5 questions from actual SSC CPO papers · all shown free · click option to reveal solution
Exam Q 12018Previous Year Pattern
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 in 2022?
Exam Q 22018Previous Year Pattern
In a city, 45% of the population is male and 55% is female. If 30% of males and 20% of females are unemployed, what percentage of the total population is unemployed?
In a town, the male population is 60% of the total. If the female population is 48,000, what is the total population of the town?
Exam Q 42018Previous Year Pattern
The population of a district increases by 25% in the first year and then by 20% in the second year. If the population after two years is 1,50,000, what was the original population?
Exam Q 52018Previous Year Pattern
A town's population was 2,50,000 in 2019. In 2020, it decreased by 8%, and in 2021, it increased by 10%. In 2022, it decreased by 5%. What is the population in 2022?
Concept Notes
Population Problems— Rules & Concept
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Core Concept
Read this first — the foundation of the topic
→CORE CONCEPT
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
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Formula Block
Memorise — at least one formula appears in every paper
Final Population = Initial Population × (1 + r/100)^n
Where:
- 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
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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
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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
COMMON MISTAKE:
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
10graded MCQs · easy to hard · full solution & trap analysis
The population of a city is 500,000. If it increases by 20% in the first year, what will be the population after one year?
Practice 2easy
A village had a population of 80,000 in 2020. If the population decreases by 15% in 2021, what is the population in 2021?
Practice 3easy
The population of town A is 250,000 and town B is 200,000. By what percentage is town A's population more than town B's?
Practice 4easy
If a city's population increases from 400,000 to 480,000, what is the percentage increase?
Practice 5easy
A region's population was 600,000 in 2019. In 2020, it became 660,000. In 2021, it became 726,000. What is the percentage increase from 2020 to 2021?
Practice 6easy
The population of a district is 1,000,000. If 35% are males and 65% are females, how many females are there?
Practice 7hard
A village's population was P in 2020. In 2021, it increased by 25%. In 2022, due to migration, it decreased by 20%. In 2023, it increased by 15%. If the population in 2023 is 11,50,000, what was the population in 2020?
Practice 8hard
A district's population comprises 60% rural and 40% urban residents. The rural population grows at 8% per annum and the urban population at 12% per annum. After 2 years, if the total population is 15,68,000, what was the original population?
Practice 9hard
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?
Practice 10hard
A town's population decreases by 15% in year 1, then increases by 20% in year 2, and finally decreases by 10% in year 3. If the population after 3 years is 1,53,000, what was the initial population?
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