Percentage Increase and Decrease: Formulas, Rules and Examples

Percentage Increase and Decrease measures how much a quantity rises or falls compared with its original value. This topic covers the percentage increase formula, percentage decrease formula, successive changes, reverse calculations and percentage change tricks. The examples use prices, salaries, populations and marks to show how to solve increase decrease questions accurately.

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What is Percentage Increase and Decrease?

Percentage increase is the rise in a quantity expressed as a percentage of its original value. Percentage decrease is the fall in a quantity expressed as a percentage of its original value.

For an increase, subtract the original value from the new value and divide by the original value. For a decrease, subtract the new value from the original value and divide by the original value. Thus, the original value is the base in both calculations. For example, if a price rises from 200 to 250, the increase is 50 and the percentage increase is (50/200) × 100 = 25%.

Percentage Increase and Decrease Formula & Tricks

Important Formulas

Percentage increase
Percentage increase = [(New value − Original value) / Original value] × 100

Use this when the new value is greater than the original value.

Percentage decrease
Percentage decrease = [(Original value − New value) / Original value] × 100

Use this when the new value is less than the original value.

New value after an increase
New value = Original value × (1 + r/100)

Here, r is the percentage increase.

New value after a decrease
New value = Original value × (1 − r/100)

Here, r is the percentage decrease.

Percentage change
Percentage change = (Change / Original value) × 100

The change is positive for an increase and negative for a decrease when using signed values.

Successive percentage changes
Net change = a + b + (ab/100), using signed percentages

Take increases as positive and decreases as negative. For example, an increase of 20% followed by a decrease of 10% gives 20 − 10 − 2 = 8% net increase.

Quick Tricks

Equal increase and decrease

An increase of x% followed by a decrease of x% always results in a net decrease of x²/100%.

Example: A 20% increase followed by a 20% decrease gives a net decrease of 20²/100 = 4%.
Use multipliers for successive changes

Convert an increase of r% into the multiplier (100 + r)/100 and a decrease of r% into (100 − r)/100. Multiply the factors to find the final value.

Example: A value of 500 increases by 10% and then decreases by 20%: 500 × 1.10 × 0.80 = 440, so the net decrease is 12%.
Find the original value from the final value

For an increase, divide the final value by 1 + r/100. For a decrease, divide the final value by 1 − r/100.

Example: After a 25% increase, a salary is 50,000. Original salary = 50,000/1.25 = 40,000.

Percentage Increase and Decrease Concepts

Finding the percentage increase

Percentage increase is calculated by dividing the increase by the original value and multiplying by 100.

First find the absolute increase: New value − Original value. Then use the original value as the denominator. If a number changes from 80 to 100, the increase is 20, so the percentage increase is (20/80) × 100 = 25%.

Example: A quantity rises from 240 to 300. Increase = 60, and percentage increase = (60/240) × 100 = 25%.

Finding the percentage decrease

Percentage decrease is calculated by dividing the decrease by the original value and multiplying by 100.

First find the absolute decrease: Original value − New value. The denominator remains the original value, not the new value. If a price falls from 500 to 425, the decrease is 75, so the percentage decrease is (75/500) × 100 = 15%.

Example: A population falls from 8,000 to 7,200. Decrease = 800, and percentage decrease = (800/8,000) × 100 = 10%.

Successive increases and decreases

Successive percentage changes are applied to the changed value, so their combined effect is generally not found by simple addition or subtraction.

For two changes a% and b%, use signed values in the formula a + b + ab/100. An increase is positive and a decrease is negative. For a 15% increase followed by a 10% increase, net change = 15 + 10 + (15 × 10)/100 = 26.5% increase.

Example: A value of 1,000 increases by 15% and then by 10%: 1,000 × 1.15 × 1.10 = 1,265. The net increase is 265/1,000 × 100 = 26.5%.

Equal percentage increase and decrease

An x% increase followed by an x% decrease produces a net decrease of x²/100%, not zero.

The increase is calculated on the original value, but the later decrease is calculated on the increased value. For an original value P, the final value is P(1 + x/100)(1 − x/100) = P(1 − x²/10,000). Therefore, the loss is x²/100% of P.

Example: If a number is increased by 10% and then decreased by 10%, the final value is 1.1 × 0.9 = 0.99 times the original value, giving a 1% decrease.

Finding the original value

To recover the original value, divide the final value by the appropriate change multiplier.

If the final value follows an r% increase, Original value = Final value/(1 + r/100). If it follows an r% decrease, Original value = Final value/(1 − r/100). The reverse percentage is not obtained by subtracting or adding the same percentage directly.

Example: After a 20% decrease, the price is 640. Original price = 640/0.80 = 800.

Percentage Increase and Decrease Video Lessons

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Percentage Increase and Decrease Using Multipliers

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Practice Percentage Increase and Decrease Questions

Practise published questions related to this topic.

1A person sells an article at the profit of 40 percent. Cost price and selling price are increased by 25 percent and 'y' percent respectively. If the new profit percentage is 20 percent, then what is the value of 'y'?→ 2What is the Least Common Multiple of all prime numbers between 5 and 12?→ 3In the records, the value is noted as 7/√7 .Simplify.→ 4A trader bought goods for ₹1200 and sold them for ₹1320. Find the profit percentage.→ 5Determine the largest number that divides both 1058 and 1550, leaving remainders of 5 and 11, respectively.→ 6DMART is offering Buy 2, get 29 free on grocery items. What is the net percentage discount being offered by DMART? (Correct up to two decimal places)→ 7Simplify: (10 × a⁵ × b⁶)/(2 × a² × b³)→ 8Two numbers are in the ratio of 3 : 5. If the Highest Common Factor of the numbers is 18, then the sum of the numbers will be _____.→ 9A shopkeeper bought six identical mobile phones for ₹ 72000, and sold two of them for ₹ 72000. Find his gain percentage.→ 10Find the least number which leaves remainder 3 when divided by 5, 7, and 8.→

Percentage Increase and Decrease Quick Quiz

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Quick Revision Notes

Percentage Increase and Decrease: Quick Revision

Use the original value as the base for a single percentage change and use multipliers for successive changes.

  • Percentage increase = [(New value − Original value)/Original value] × 100.
  • Percentage decrease = [(Original value − New value)/Original value] × 100.
  • After an r% increase, multiply by (1 + r/100).
  • After an r% decrease, multiply by (1 − r/100).
  • For successive changes, use a + b + ab/100 with increases positive and decreases negative.
  • An x% increase followed by an x% decrease gives an x²/100% net decrease.
  • To find the original value after an increase, divide by 1 + r/100.
  • To find the original value after a decrease, divide by 1 − r/100.

Percentage Increase and Decrease FAQs

What is the percentage increase formula?

Percentage increase = [(New value − Original value)/Original value] × 100. For a change from 400 to 460, the increase is 60, so the percentage increase is 15%.

What is the percentage decrease formula?

Percentage decrease = [(Original value − New value)/Original value] × 100. A fall from 800 to 680 gives (120/800) × 100 = 15% decrease.

What is the net effect of a 25% increase followed by a 20% decrease?

Use signed successive changes: 25 − 20 + (25 × −20)/100 = 0%. The final value is equal to the original value.

Why does a 10% increase followed by a 10% decrease result in a 1% loss?

The multipliers are 1.10 and 0.90. Their product is 0.99, so the final value is 99% of the original and the net decrease is 1%.

A number becomes 1,500 after a 50% increase. What was the original number?

Original number = 1,500/1.5 = 1,000.

A price becomes 720 after a 10% decrease. What was its original price?

Original price = 720/0.90 = 800.

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