Study Material — 14 PYQs (2020–2020) · Concept Notes · Shortcuts
SBI PO Population Problems is a frequently tested subtopic — 14 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.
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?
Exam Q 42020Previous Year Pattern
A village had a population of 80,000 in 2019. The population decreased by 15% in 2020. What was the population at the end of 2020?
Exam Q 52020Previous Year Pattern
The population of a town was 250,000 in 2018. It increased by 10% in 2019 and then increased by 20% in 2020. What was the population at the end of 2020?
Exam Q 62020Previous Year Pattern
A city's population was 400,000 in 2015. If the population increased to 480,000 by 2018, what was the percentage increase?
Exam Q 72020Previous Year Pattern
In a state, the population increased by 15% from 2010 to 2015, and then decreased by 10% from 2015 to 2020. If the population in 2020 was 20,70,000, what was the population in 2010?
Exam Q 82020Previous Year Pattern
In a district, the male population is 55% of the total population. If the total population is 8,00,000, how many females are there in the district?
Exam Q 92020Previous Year Pattern
A city's population grows from 6,00,000 to 7,26,000 over two years with the same percentage growth rate each year. What is the annual growth rate?
Exam Q 102020Previous Year Pattern
The population of a city increases by 20% in the first year and by 25% in the second year. If the population after 2 years is 3,60,000, what was the initial population?
Exam Q 112020Previous Year Pattern
A town's population was 5,00,000 in 2015. It decreased by 10% in 2016 and then increased by 20% in 2017. What is the population in 2017?
Exam Q 122020Previous Year Pattern
The population of village A is 40% more than village B. If village B has a population of 50,000, what is the population of village A?
Exam Q 132020Previous Year Pattern
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?
Exam Q 142020Previous Year Pattern
A village's population was P in 2020. In 2021, it increased by x%. In 2022, it decreased by (x-5)%. If the population in 2022 is 2,00,200 and equals 91% of the 2020 population, find x.
Concept Notes
Population Problems— Rules & Concept
💡
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
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