Maths · KS3 and GCSE · Interactive lesson
Finding an original amount: reverse percentages
Work backwards from a sale price or an increased price. Find what percentage remains, then calculate the original amount.
Choose your view
Explore an interactive example, then try the questions at your own pace.
Later KS3 / GCSE
By the end of this lesson: Find the original amount before a percentage change.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- The original price represents 100%.
- A 20% discount leaves the final price 80% of the original.
- Work back from £80: find 1%, then 100%.
Useful starting points
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What do the words mean?
- Discount
- A reduction in the price.
- Multiplier
- A number you multiply by. For example, 0.8 keeps 80% of an amount.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the percentage the same. Increase the final price. What happens to the original price?
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
Both bars compare with the original price, which is 100%. Prices are rounded to the nearest penny when needed. ≈ means approximately equal.
More about this diagram
Still picture. Play particle motion in Stage 2.
Original price = £100
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- The final price, £80, represents 80% of the original.
- Find 1%: £80 ÷ 80 = £1.
- Find 100%: (£80 ÷ 80) × 100. Use the unrounded value of 1%.
- Original price = £100.00. Round the price at the end, to the nearest penny.
Try on your own
Your turn. No rush.
Question 1
A coat costs £80 after a 20% discount. What was its original price?
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
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Can you say which percentage the final amount represents?
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
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