Population Percentage: Formula, Questions and Tricks

Population Percentage problems calculate population growth, decline, or the original population after a percentage change. The main method uses a multiplier: increase by r% means multiplying by 1 + r/100, while decrease by r% means multiplying by 1 − r/100. These rules solve common population percentage questions and percentage word problems.

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What Is Population Percentage?

Population percentage refers to calculating a population after a percentage increase or decrease, or finding the original population from a changed value. For an initial population P and a rate r%, the new population is P(1 ± r/100).

Use the plus sign for population growth and the minus sign for population decline. If the initial population is 40,000 and it increases by 8%, the new population is 40,000 × 1.08 = 43,200. If it decreases by 8%, the population becomes 40,000 × 0.92 = 36,800.

Population Percentage Formula & Tricks

Important Formulas

Population after increase
New population = P × (1 + r/100)

P is the initial population and r is the percentage increase.

Population after decrease
New population = P × (1 − r/100)

P is the initial population and r is the percentage decrease.

Percentage change
Percentage change = [(New population − Old population) / Old population] × 100

A positive result indicates growth and a negative result indicates decline.

Original population after increase
Original population = New population ÷ (1 + r/100)

Use this formula when the final population and percentage increase are given.

Original population after decrease
Original population = New population ÷ (1 − r/100)

Use this formula when the final population and percentage decrease are given.

Successive population changes
Final population = P × (1 + r₁/100) × (1 + r₂/100)

Use the relevant multiplier for each successive increase or decrease; use a minus sign for a decrease.

Quick Tricks

Use a multiplier instead of finding the change separately

An increase of r% changes the population to (100 + r)% of the original. A decrease of r% changes it to (100 − r)% of the original.

Example: A population of 25,000 increasing by 12% becomes 25,000 × 112/100 = 28,000.
Reverse the multiplier for the original population

Do not subtract the percentage directly from the final population. Divide by the appropriate multiplier.

Example: If the population after a 20% increase is 36,000, the original population is 36,000 ÷ 1.20 = 30,000.
Combine successive changes by multiplication

Successive percentage changes are applied to the changed population, so their multipliers must be multiplied.

Example: A 10% increase followed by a 20% increase gives 1.10 × 1.20 = 1.32, or a total increase of 32%.

Population Percentage Concepts

Population Growth

For a population that increases by r%, multiply the original population by (100 + r)/100.

The increase in population is P × r/100, so the final population is P + P × r/100 = P(1 + r/100).

Example: If a town has 60,000 people and grows by 5%, the increase is 3,000 and the new population is 63,000.

Population Decline

For a population that decreases by r%, multiply the original population by (100 − r)/100.

The decrease is P × r/100, so the final population is P − P × r/100 = P(1 − r/100).

Example: If a district has 80,000 people and its population falls by 15%, the new population is 80,000 × 0.85 = 68,000.

Finding the Original Population

To find the population before a percentage change, divide the final population by the applicable multiplier.

After an increase of r%, the multiplier is 1 + r/100. After a decrease of r%, it is 1 − r/100. The final value must not be reduced by the percentage directly because the percentage is based on the original population.

Example: A city has 54,000 people after a 10% decrease. Its original population was 54,000 ÷ 0.90 = 60,000.

Successive Increase and Decrease

For successive population changes, apply each percentage to the population obtained after the previous change.

For an increase of a% followed by a decrease of b%, the final population is P(1 + a/100)(1 − b/100). The net percentage change is found by comparing this result with P.

Example: If P = 50,000, followed by a 10% increase and a 10% decrease, the final population is 50,000 × 1.10 × 0.90 = 49,500, a net decrease of 1%.

Population Comparison and Percentage Difference

When comparing two populations, the percentage increase or decrease is calculated using the original or reference population as the denominator.

If population A changes to population B, percentage change = (B − A)/A × 100. For a comparison such as how much larger A is than B, use B as the reference only if the question states that B is the base.

Example: If one village has 24,000 people and another has 20,000, the first is (4,000/20,000) × 100 = 20% larger than the second.

Population Percentage Video Lessons

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Population-Based Percentage Problems

Learn to solve percentage problems involving population changes, including increases, decreases, and comparisons, using clear step-by-step quantitative aptitude methods.

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Practice Population Percentage Questions

Practise published questions related to this topic.

1A school drum beats every 12 minutes, and the school bell rings every 18 minutes. If both sounded together at 9:00 AM, how many times will they sound together again before 11:00 AM?→ 2During a sale, 50% of the goods are sold at 21% profit, 30% of the remaining goods are sold at 43% profit and the still remaining goods are sold at a loss of 17%. If there is an overall profit of x%, then what is the value of x?→ 3If a four-digit number 34X1 is divisible by 7, then X2 is:→ 4A dealer purchased a ceiling fan for ₹391. After allowing a discount of 31% on its marked price, he still gains 68%. Find the marked price of the ceiling fan.→ 5Find the value of x in the following expression. (0.36)³ × (0.216)³ ÷ (0.1296)³ = (60 ÷ 100)^(x+1)→ 6A person sold an article at a loss of 10%. Had he sold it for ₹60 more, he would have gained 5%. Find the cost price of the article.→ 7Selling price and cost price of an article is Rs. 4000 and Rs. 5000 respectively. What is the loss percentage?→ 8If the ratio of two numbers is 6 : 7, and their HCF is 9, then their LCM is:→ 9The product of two numbers is 328 and their LCM is 164. Find their HCF.→ 10Which is the largest number that divides 122, 146, 170 and 194 to leave the same remainder in each case?→

Population Percentage Quick Quiz

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Quick Revision Notes

Population Percentage Revision Points

Use these formulas and rules for quick revision of population percentage calculations.

  • Increase by r%: New population = P(1 + r/100).
  • Decrease by r%: New population = P(1 − r/100).
  • Original after increase: Final population ÷ (1 + r/100).
  • Original after decrease: Final population ÷ (1 − r/100).
  • Successive changes are applied through multiplication, not simple addition in every case.
  • Percentage change is measured with respect to the original or stated reference population.
  • An equal percentage increase and decrease do not cancel; an increase of r% followed by a decrease of r% gives a net decrease of r²/100%.

Population Percentage FAQs

What is the population percentage formula for an increase?

New population = Original population × (1 + percentage increase/100). For 30,000 increased by 10%, the result is 30,000 × 1.10 = 33,000.

What is the population percentage formula for a decrease?

New population = Original population × (1 − percentage decrease/100). For 50,000 decreased by 12%, the result is 50,000 × 0.88 = 44,000.

How do you find the original population after a 25% increase?

Divide the final population by 1.25. For a final population of 75,000, the original population is 75,000 ÷ 1.25 = 60,000.

A population increases by 20% and then decreases by 20%. What is the net change?

The multiplier is 1.20 × 0.80 = 0.96. Therefore, the final population is 96% of the original, giving a net decrease of 4%.

A population changes from 45,000 to 54,000. What is the percentage increase?

Percentage increase = (54,000 − 45,000) ÷ 45,000 × 100 = 20%.

How is a population percentage increase different from percentage points?

A population percentage increase compares the new population with the original population. Percentage points describe the direct difference between two percentages, such as a change from 40% to 50%, which is 10 percentage points.

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