GCSE & IGCSE maths practice

Reverse percentages questions and answers

In a reverse percentage question you know the amount after a percentage change and need the original. Write the new amount as a multiplier of the original, then divide: original = new amount ÷ multiplier. After a 20% increase, the new amount is 120% of the original, so divide by 1.2.

15 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 10 Nov 2026.

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Where reverse percentages comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: solve original value problems (reverse percentages).
Cambridge IGCSE (0580)	Extended only: calculate using reverse percentages.

The method

Work out the multiplier for the change (e.g. 20% increase → 1.2; 30% off → 0.7).
Original = new amount ÷ multiplier.
Check by applying the percentage to your answer.

Reverse percentages questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

After a 20% increase, a price is £60. What was the original price?

Question 2Warm-upFoundation

After a 25% decrease, a value is 90. What was the original value?

Question 9Warm-upFoundation

After a 10% increase, a price is £44. What was the original price?

Question 10Warm-upFoundation

After a 50% decrease, a value is 35. What was the original value?

Exam-style

Question 3Exam-styleFoundation

In a 30% off sale, a jacket costs £56. What was its original price?

Question 4Exam-styleFoundation

A bike costs £96 including VAT at 20%. What is its price without VAT?

Question 5Exam-styleFoundation

After a 15% increase, a population is 230. What was it before?

Question 6Exam-styleFoundation

After a 4% pay rise, a salary is £26 000. What was it before the rise?

Question 11Exam-styleFoundation

In a 40% off sale, a pair of trainers costs £27. What was the original price?

Question 12Exam-styleFoundation

A phone costs £150 including VAT at 20%. What is the price before VAT?

Question 13Exam-styleFoundation

After an 8% decrease, the number of visitors is 460. How many were there before?

Challenge

Question 7ChallengeFoundation

An investment grows by 10% each year. After 2 years it is worth £242. What was it worth at the start?

Question 8ChallengeFoundation

A value is decreased by 12% to give 176. What was the original value?

Question 14ChallengeFoundation

A car has lost 15% of its value and is now worth £10 200. What was it worth when new?

Question 15ChallengeFoundation

A price is increased by 25%, then the new price is decreased by 20%. The final price is £60. What was the original price?

Common mistakes

Taking the percentage off the new amount (20% less than £60 isn't the original).
Using the wrong multiplier for a decrease.
Dividing by the percentage (e.g. 120) instead of the multiplier (1.2).

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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