Reverse percentages: GCSE practice questions

Eighteen questions with complete worked answers — foundation through to higher tier. Nothing is gated and there is no sign-up. Answers stay hidden until you open them, so the page works as practice, and the printable version includes the full working for marking.

Printable worksheet (PDF)

The same 18 questions with a full answer key, branded and classroom-ready. Free to reproduce for teaching with attribution.

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Before you start

Every question below is the same shape: you are told what a value became, and asked what it was. Write the multiplier on its own line first — 85% = 0.85 — then divide. That single line is where the method marks live, and it survives an arithmetic slip at the final step.

Check each answer by going forwards. Reversing a discount must give a bigger number than the one in the question; reversing an increase must give a smaller one. If your answer sits on the wrong side, you multiplied where you should have divided, and you will catch it in seconds rather than losing the marks.

The higher-tier questions layer two changes. Multiply the multipliers together and divide once by the product — never add or subtract the percentages, and never divide twice with rounding in between.

Exercise book showing the wrong attempt £68 + 15% crossed out, and the correct working £68 ÷ 0.85 = £80 with a tick. — What the marks look like: the multiplier written down, one division, and a forwards check — not the crossed-out shortcut.

Foundation

Single changes, friendly numbers.

Q1. A coat costs £48 in a sale after a 20% discount. What was the original price?
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Answer: £60
1. 100% − 20% = 80%, so £48 is 80% of the original
2. 48 ÷ 0.8 = 60
3. Check: £60 − 20% = £48 ✓
Q2. After a 10% increase, a bus fare is £2.20. What was it before?
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Answer: £2.00
1. 100% + 10% = 110%, so £2.20 is 110% of the original
2. 2.20 ÷ 1.1 = 2.00
Q3. A jacket is reduced by 25% to £45. Find the original price.
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Answer: £60
1. 75% remains
2. 45 ÷ 0.75 = 60
Q4. 30 is 40% of a number. What is the number?
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Answer: 75
1. Unitary method: 40% = 30, so 1% = 30 ÷ 40 = 0.75
2. 100% = 0.75 × 100 = 75
Q5. A phone bill rose by 5% to £42. What was the bill before the rise?
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Answer: £40
1. 42 ÷ 1.05 = 40

Crossover

VAT, pay rises and depreciation.

Q6. A laptop costs £540 including 20% VAT. What is the price excluding VAT?
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Answer: £450
1. The gross price is 120% of the net price
2. 540 ÷ 1.2 = 450
3. The VAT is £540 − £450 = £90
Q7. After a 12% pay rise, Amira earns £28,000. What did she earn before?
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Answer: £25,000
1. 28,000 ÷ 1.12 = 25,000
Q8. A car is now worth £7,200 after losing 40% of its value. What was it worth new?
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Answer: £12,000
1. 60% of the original remains
2. 7,200 ÷ 0.6 = 12,000
Q9. A test score of 68% earned 51 marks. How many marks were available?
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Answer: 75 marks
1. 51 ÷ 0.68 = 75
Q10. A shop reduces everything by 15%. A lamp now costs £38.25. Find its original price.
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Answer: £45
1. 85% remains
2. 38.25 ÷ 0.85 = 45
Q11. A population fell by 8% to 11,500. What was it before the fall?
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Answer: 12,500
1. 92% remains
2. 11,500 ÷ 0.92 = 12,500
Q12. A restaurant bill including a 12.5% service charge comes to £81. What was the bill before service?
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Answer: £72
1. 81 ÷ 1.125 = 72
2. The service charge is £81 − £72 = £9

Higher

Consecutive changes and increases above 100%.

Q13. A price is increased by 20% and then reduced by 20%. The final price is £96. What was the original?
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Answer: £100
1. Do NOT assume the changes cancel — they do not
2. The combined multiplier is 1.2 × 0.8 = 0.96
3. 96 ÷ 0.96 = 100
4. Note the item is now cheaper than it started, despite equal percentages
Q14. An investment grows by 6% in year one and 4% in year two, reaching £11,024. What was invested?
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Answer: £10,000
1. Combined multiplier = 1.06 × 1.04 = 1.1024
2. 11,024 ÷ 1.1024 = 10,000
Q15. After two consecutive 10% reductions, a bike costs £324. Find the original price.
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Answer: £400
1. 0.9 × 0.9 = 0.81
2. 324 ÷ 0.81 = 400
Q16. A sofa costs £660 including 20% VAT, after a 12% discount was applied to the net price. What was the net price before the discount?
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Answer: £625
1. Remove VAT first: 660 ÷ 1.2 = £550 net after discount
2. Then remove the discount: 88% remains, so 550 ÷ 0.88 = £625
3. Order matters — removing the discount first would give the wrong answer
Q17. The number of members increased by 150% to 500. How many members were there before?
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Answer: 200
1. An increase of 150% means the new figure is 250% of the old
2. 500 ÷ 2.5 = 200
Q18. A shop claims "was £80, now £60". What percentage discount is that, and what price would a further 25% off give?
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Answer: 25% off; £45
1. Reduction = 20 ÷ 80 = 0.25 = 25%
2. A further 25% off £60: 60 × 0.75 = £45
3. The two 25% reductions do NOT total 50% off £80 (which would be £40)

Frequently asked questions

›What is a reverse percentage in GCSE maths?

A question that gives you the value after a percentage change and asks for the value before it. You divide by the multiplier rather than applying the percentage again.

›Are reverse percentages on the foundation or higher paper?

Both. Foundation questions usually involve a single change with friendly numbers; higher papers add consecutive changes, VAT combined with a discount, and increases above 100%.

›How many marks are reverse percentage questions worth?

Typically 2 to 4. Method marks are available for identifying the correct multiplier even if the final arithmetic slips, which is why writing the multiplier down first is worth doing.

›Do two consecutive percentage changes cancel out?

No. A 20% increase followed by a 20% decrease gives 1.2 × 0.8 = 0.96, so you end up 4% below where you started. This is one of the most commonly examined misconceptions.

›Is there a free reverse percentages worksheet with answers?

Yes. Every question on this page has full worked answers shown, and the same set is available as a printable PDF with the working included.

New to the topic? Start with how to do reverse percentages, or check your working with the calculator.