CDS Population Problems — Study Material, 7 PYQs & Practice MCQs | ZestExam
ZestExam
CDS Population Problems
Study Material — 7 PYQs (2018–2020) · Concept Notes · Shortcuts
CDS 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.
7 questions from actual CDS 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?
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 32020Previous 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 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 52019Previous 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 62019Previous 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?
Exam Q 72020Previous 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?
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
🔢
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
📊
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
41graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 41
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 2easy
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 3easy
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 4easy
A state's population increases by 25% to reach 1,250,000. What was the original population?
Practice 5easy
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 6easy
If a population increases from 250,000 to 300,000, what is the percentage increase?
Practice 7easy
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 8easy
A village population increased from 80,000 to 96,000 over two years. What was the percentage increase in population?
Practice 9easy
A village had a population of 80,000 in 2020. The population decreased by 15% in 2021. What was the population in 2021?
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
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 12easy
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 13easy
If a region's population was 600,000 last year and it is now 660,000, what is the percentage increase?
Practice 14easy
A city's population grows from 400,000 to 480,000 over one year. What is the percentage growth rate?
Practice 15easy
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 16easy
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 17easy
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 18easy
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 19medium
In a town, the male population is 55% of the total population. If the female population is 180,000, what is the total population of the town?
Practice 20medium
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?
21 more practice questions in the Study Panel
Difficulty-graded, bookmarkable, with timed mode. Free account — no credit card.