Population Growth: Formula, Percentage Increase and Questions

Population Growth questions use percentage increase or decrease to calculate a future population, the original population, or the growth rate. This page explains the population growth formula, multiplier method, successive annual growth, population decrease and reverse calculations with clear numerical examples.

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What Is Population Growth?

Population growth is the change in population expressed as a percentage of the original population. If the population increases by r%, the new population is the original population multiplied by 1 + r/100.

For an original population P and a growth rate of r%, the increase is P × r/100, and the new population is P(1 + r/100). For a decrease of r%, the new population is P(1 − r/100). For example, a population of 20,000 growing by 15% becomes 20,000 × 1.15 = 23,000.

Population Growth Formula & Tricks

Important Formulas

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

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

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

Use this multiplier when the population falls by r%.

Population increase percentage
Percentage increase = [(New population − Original population) / Original population] × 100

The original population is used as the denominator.

Population after n years
Final population = P × (1 + r/100)^n

Use this when the population grows at the same annual rate r% for n years.

Original population
Original population = Final population / (1 + r/100)^n

Use the reverse multiplier to find the population before n years of growth.

Two successive growth rates
Net percentage change = a + b + (ab/100)

For successive increases of a% and b%, the net increase is this value.

Quick Tricks

Use a growth multiplier

Convert an increase of r% into the multiplier 1 + r/100 and a decrease of r% into 1 − r/100. This avoids calculating separate changes repeatedly.

Example: A population of 8,000 increases by 25%: 8,000 × 1.25 = 10,000.
Apply successive changes in sequence

For different annual rates, multiply the corresponding factors. Do not simply add the rates unless the question involves successive percentage increases using the net-change formula.

Example: A population increases by 10% and then 20%: multiplier = 1.10 × 1.20 = 1.32, so the net increase is 32%.
Reverse the percentage change

To find the earlier population, divide the later population by the growth multiplier instead of subtracting the same percentage from the later value.

Example: If the population after a 25% increase is 50,000, the original population is 50,000 ÷ 1.25 = 40,000.

Population Growth Concepts

Population Increase by a Given Percentage

When a population increases by r%, the increase equals P × r/100 and the new population equals P(1 + r/100).

The percentage increase is always calculated on the original population. If P = 12,000 and r = 8%, increase = 12,000 × 8/100 = 960. Therefore, new population = 12,000 + 960 = 12,960, or 12,000 × 1.08.

Example: A town with 30,000 people grows by 12%. Its new population is 30,000 × 1.12 = 33,600.

Population Growth Over Several Years

If the same annual growth rate applies each year, multiply the population by the growth factor for every year: P(1 + r/100)^n.

The second year's growth is calculated on the first year's population, not on the original population. For a population of 10,000 growing by 10% for 2 years, final population = 10,000 × 1.10² = 12,100.

Example: A city's population is 40,000 and grows by 5% annually for 3 years. Final population = 40,000 × 1.05³ = 46,305.

Successive Growth Rates

For two successive increases of a% and b%, the total increase is a + b + ab/100 percent.

The product term ab/100 represents the second increase being applied to the population after the first increase. Thus, increases of 20% and 10% give a net increase of 20 + 10 + (20 × 10)/100 = 32%.

Example: A population of 25,000 rises by 20% and then by 10%. Final population = 25,000 × 1.20 × 1.10 = 33,000.

Population Decrease and Reverse Calculation

After a decrease of r%, the population becomes P(1 − r/100); to find the original population after an increase, divide the final population by the growth factor.

A decrease is not reversed by adding the same percentage to the reduced population. If a population falls by 20%, it becomes 80% of its original value. If the final value is known after a 20% increase, divide by 1.20 to find the original value.

Example: A population decreases from 50,000 by 16%. New population = 50,000 × 0.84 = 42,000. If 42,000 is the population after a 16% decrease, the original population is 42,000 ÷ 0.84 = 50,000.

Population Growth 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 Growth Questions

Practise published questions related to this topic.

1Find the simplified value of the given expression. ((2³ × 8²)³ ÷ (4⁵ × 16²))/((32² ÷ 2⁴)²)→ 2An 8-digit number is divisible by 45. If the digits are rearranged, then the number must be divisible by:→ 3Selling price and cost price of an article is Rs. 550 and Rs. 500 respectively. What is the profit percentage?→ 4If the ratio of two numbers is 3 : 8, and their HCF is 6, then their LCM is:→ 5After allowing a discount of 9% on the marked price of an article, it is sold for ₹53,053. Find its marked price (in ₹).→ 6A T-shirt is on sale for 15% off its original price of Rs 60. How much will you pay for the T-shirt?→ 7(√32 + √162)/√18 = ?→ 8Which of the following number is NOT divisible by 8?→ 9What is the Highest Common Factor of 0.42, 0.60 and 0.78?→ 10A retailer offers the following discount schemes for buyers on an article. Which scheme will fetch the maximum selling price?→

Population Growth Quick Quiz

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Quick Revision Notes

Population Growth Revision Points

Use the original population as the base for a single percentage change and use multipliers for repeated changes.

  • Increase by r%: multiply by 1 + r/100.
  • Decrease by r%: multiply by 1 − r/100.
  • For n equal annual increases: Final population = P(1 + r/100)^n.
  • For successive increases a% and b%: net increase = a + b + ab/100%.
  • To find the original population after growth, divide by the growth multiplier.
  • For different yearly rates, multiply each yearly factor separately.
  • Percentage increase = change divided by original population, multiplied by 100.

Population Growth FAQs

What is the population growth formula?

For an increase of r% from an original population P, the formula is New population = P(1 + r/100). For example, 16,000 growing by 5% becomes 16,000 × 1.05 = 16,800.

How is population increase percentage calculated?

Population increase percentage = [(New population − Original population) ÷ Original population] × 100. If the population rises from 24,000 to 27,000, the increase percentage is (3,000 ÷ 24,000) × 100 = 12.5%.

What is the population after 3 years at an annual growth rate of 10%?

Use P(1.10)^3. Thus, a population of 20,000 becomes 20,000 × 1.10³ = 26,620.

How do you find the original population after a 20% increase?

Divide the final population by 1.20. If the final population is 36,000, the original population is 36,000 ÷ 1.20 = 30,000.

What is the net effect of successive population increases of 15% and 20%?

Net increase = 15 + 20 + (15 × 20)/100 = 38%. The combined multiplier is 1.15 × 1.20 = 1.38.

Is a 20% increase followed by a 20% decrease equal to no change?

No. The combined multiplier is 1.20 × 0.80 = 0.96, so there is a net decrease of 4%. For an original population of 10,000, the final population is 9,600.

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