Learn the 3-Step Method
1Work out what % the price represents.
After 25% off, you pay 100 − 25 = 75% of the original.
2Find an easy block.
75% = £45, so 25% = 45 ÷ 3 = £15.
3Scale up to 100%.
100% = 4 × £15 = £60.
Worked Example
After a 10% price rise, a ticket costs £22. What did it cost before?
Watch Out! Common Mistakes
Wrong! The 25% was of the original, not of £45. Working back properly gives £60.
Wrong! After 25% off, £45 is 75% of the original.
Always check! Run your answer forwards: £60 − 25% = £45 ✓. If it doesn’t reproduce the question, start again.
⬇ Cheat Sheet
- Decide what % the given price represents (100 − discount, or 100 + rise).
- Divide to find an easy block (1%, 10% or 25%).
- Scale up to 100% — that's the original.
- Check by running the problem forwards.
📖 Continue Your Journey
Quick summary
- Decide what percentage the known price represents (75% after 25% off; 110% after a 10% rise).
- Divide to find one easy block — 1%, 10% or 25%.
- Scale up to 100% to find the original.
- Always check by running the problem forwards.
Frequently asked questions
What is a reverse percentage question?
One where you know the amount after a percentage change and must find the original — like a sale price of £45 after 25% off (original: £60).
Why can't you just add the percentage back on?
Because the discount was a percentage of the original, not of the sale price. Adding 25% of £45 gives £56.25 — the wrong answer.
Are reverse percentages on the KS2 curriculum?
They're beyond the standard Year 6 objectives but appear in grammar-school 11+ papers, so we include them as a clearly-marked stretch lesson.
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