To increase or decrease by a percentage, multiply by a decimal multiplier: a 15% decrease is × 0.85 and a 3.5% increase is × 1.035. To find a percentage change, divide the change by the original amount and multiply by 100. Successive percentage changes are applied one after another by multiplying by each multiplier, which is why a 10% rise followed by a 10% fall does not get you back to the start.
Percentage change
- Increase by p%: × (1 + p/100)
- Decrease by p%: × (1 − p/100)
- Percentage change = (change ÷ original) × 100
- Profit or loss: compare with the cost price
- Successive changes: multiply the multipliers
Increasing and decreasing with multipliers
Add the percentage to 100% for an increase, or subtract it for a decrease, then write the result as a decimal. A 15% decrease leaves 85%, so multiply by 0.85; a 3.5% increase gives 103.5%, so multiply by 1.035. One multiplication gives the new amount directly.
Working out a percentage change
To find the percentage change, divide the change by the original amount, then multiply by 100. If a value falls from 250 to 210, the change is 40, and 40 ÷ 250 × 100 = 16%, a 16% decrease. Always divide by the original amount, not the new one.
Profit and loss
In profit and loss questions, the original amount is the cost price. If an item bought for £40 is sold for £52, the profit is £12, and the percentage profit is 12 ÷ 40 × 100 = 30%.
Successive percentage changes
To apply two changes in turn, multiply by both multipliers. A price of £600 increased by 10% and then decreased by 10% becomes 600 × 1.1 × 0.9 = £594, not £600, because the second change is a percentage of a bigger amount.
Choosing the right method
If you know the original and the percentage, multiply to find the new amount. If you know the original and new amounts, find the percentage change. If you know the new amount and the percentage, you need a reverse percentage, dividing by the multiplier.
Worked examples
Example 1. A coat costs £90. In a sale it is reduced by 15%. Work out the sale price.
- Multiplier: 1 − 0.15 = 0.85.
- 90 × 0.85.
Answer: £76.50.
Example 2. Increase £240 by 3.5%.
- Multiplier: 1.035.
- 240 × 1.035.
Answer: £248.40.
Example 3. A value falls from 250 to 210. Work out the percentage decrease.
- Change: 250 − 210 = 40.
- 40 ÷ 250 × 100.
Answer: 16%.
Example 4. A shop buys a lamp for £40 and sells it for £52. Work out the percentage profit.
- Profit: £12.
- 12 ÷ 40 × 100.
Answer: 30%.
Example 5. A price of £600 is increased by 10%, and the new price is then decreased by 10%. Work out the final price.
- 600 × 1.1 = 660.
- 660 × 0.9.
Answer: £594.
Common mistakes
- Dividing by the new amount. Percentage change always uses the original amount.
- Using 0.15 as the decrease multiplier. A 15% decrease is × 0.85.
- Assuming successive changes cancel. +10% then −10% gives 99% of the original.
- Writing 1.25 for a 2.5% increase. 2.5% is 0.025, so the multiplier is 1.025.
- Using the selling price as the original. Profit percentage compares with the cost price.
How percentage change is examined
Percentage change and profit and loss questions appear on both tiers of the Edexcel GCSE (1MA1) and International GCSE (4MA1), very often in real-life contexts. Questions ask you to:
- increase or decrease an amount by a percentage using a multiplier
- work out a percentage increase, decrease, profit or loss
- apply two percentage changes in turn
- decide which of two offers is better
The percentage change worksheet includes answers, and the GCSE proportion revision engine gives unlimited practice.
This builds on percentages and leads to reverse percentages and growth and decay.
Frequently asked questions
How do you calculate a percentage change?
Divide the change by the original amount, then multiply by 100.
What multiplier gives a 3.5% increase?
1.035.
Why does a 10% increase followed by a 10% decrease not return to the original?
Because the 10% decrease is taken from the larger, increased amount: 1.1 × 0.9 = 0.99.