Study Material — 3 PYQs (2021–2021) · Concept Notes · Shortcuts
IBPS RRB PO Population Problems is a frequently tested subtopic — 3 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
IBPS RRB PO Population Problems — Past Exam Questions
3 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution
Exam Q 12021Previous Year Pattern
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 22021Previous 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 32021Previous Year Pattern
The population of a town increased from 200,000 to 250,000 over one year. What was the percentage increase in population?
Concept Notes
Population Problems— Rules & Concept
Core ConceptRead 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
Formula BlockMemorise — 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
Exam PatternsWhat 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
Worked ExampleSolve 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
Exam TrapsCommon 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
12graded MCQs · easy to hard · full solution & trap analysis
The population of a region was 600,000 in 2010. If the population increased to 750,000 by 2015, what was the percentage increase over this 5-year period?
Practice 2easy
In 2018, a district had 300,000 people. By 2019, the population increased by 10%, and by 2020, it increased by another 20% on the 2019 population. What was the population in 2020?
Practice 3easy
A city's population was 400,000 in 2015. If the population decreased by 5% in 2016 and then increased by 10% in 2017 (on the 2016 population), what was the population in 2017?
Practice 4medium
In a town, 35% of the population are children and 45% are adults. The remaining population are seniors. If there are 16,000 seniors, what is the total population?
Practice 5medium
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?
Practice 6medium
A city's population was 600,000 in 2019. In 2020, it increased by 25%, and in 2021, it decreased by 20%. What is the net percentage change from 2019 to 2021?
Practice 7medium
The population of a district increased from 250,000 to 280,000 over 5 years. What is the percentage increase in population?
Practice 8medium
In a town, the male population is 60% of the total. If the female population is 8,000, what is the total population of the town?
Practice 9medium
A village population grows at 15% per annum. If the current population is 40,000, what will be the population after 2 years (assuming compound growth)?
Practice 10hard
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 11hard
A village population decreases by 10% in year 1, increases by 20% in year 2, and decreases by 25% in year 3. If the final population is 1,62,000, what was the population at the start of year 2 (after year 1 decrease)?
Practice 12hard
A state's population grows such that it becomes 1.5 times in 10 years. If this growth rate continues, what percentage of the original population will the population be after 20 years?
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