RRB Group D Population Problems — Study Material, 4 PYQs & Practice MCQs | ZestExam
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RRB Group D Population Problems
Study Material — 4 PYQs (2021–2021) · Concept Notes · Shortcuts
RRB Group D Population Problems is a frequently tested subtopic — 4 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
RRB Group D Population Problems — Past Exam Questions
4 questions from actual RRB Group D papers · all shown free · click option to reveal solution
Exam Q 12021Previous 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 at the end of 2022?
In a city, 45% of the population are children and 30% are elderly. If there are 50,000 working-age adults, what is the total population of the city?
Exam Q 32021Previous Year Pattern
The population of a district increased by 25% in the first year and by 20% in the second year. If the population at the end of the second year is 3,60,000, what was the initial population?
Exam Q 42021Previous Year Pattern
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?
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
✏️
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
3graded MCQs · easy to hard · full solution & trap analysis
The population of a town was 50,000 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?
Practice 2medium
The population of a town was 80,000 in 2020. It increased by 15% in 2021 and then decreased by 10% in 2022. What is the population at the end of 2022?
Practice 3hard
The population of a city was 5,00,000 in 2015. It increased by 20% in the next 4 years (by 2019). However, due to migration, the population decreased by 10% in the next 2 years (by 2021). In 2022, the population increased by 5%. What is the percentage change in the population from 2015 to 2022?
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