A percentage means a number of parts out of one hundred. Writing a percentage as a decimal multiplier makes changes easier to calculate. An increase keeps the whole original amount and adds a percentage of it; a decrease keeps what remains. Reverse percentage questions work backwards from the changed amount, so divide by the multiplier rather than subtracting a percentage of the new value. For repeated changes, each percentage acts on the latest amount. This means two increases of 10% are not the same as one increase of 20%.
Learning objectives
- Use multipliers for percentage increases and decreases.
- Reverse a change and calculate repeated percentage changes.
Key ideas
A percentage means a fraction out of one hundred.
Multiply by the appropriate change multiplier.
For a non-zero multiplier, divide the changed amount to recover the original.
Repeated changes apply to the current amount; multiply by every multiplier in sequence.
A full percentage decrease leaves zero; its original amount cannot be recovered from that zero alone.
Worked examples
Example 1
A coat costs fifty-four pounds after a quarter-price discount. Find its original price.
Check by applying the discount.
Answer
Example 2
Find the amount after two years of annual compound interest.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Find a percentage, a percentage change or a new amount.
AO2 · Reasoning
Explain why equal percentage increases and decreases do not cancel.
AO3 · Problem solving
Compare offers or combine consecutive percentage changes.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
A reverse percentage is not undone by adding the same percentage. Divide by the original multiplier.
Try it yourself
Attempt each question before opening its answer.
Check 1: Increase £80 by 15%.
Answer: £92
Use multiplier 1.15: £80 × 1.15 = £92.
Check 2: £200 earns 5% compound interest each year. What is the amount after 2 years?
Answer: £220.50
Multiply twice by 1.05: £200 × 1.05 × 1.05 = £220.50.
Explain it in your own words
- Write the multipliers for a 12% increase and a 12% decrease.
- Explain why adding 25% to £54 does not undo a 25% discount.
- Compare two increases of 10% with one increase of 20%.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Ratio specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.