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GCSE Maths / Edexcel

Reverse percentages

Find the original value when the final value after a percentage increase or decrease is given.

Number and Place ValueFoundation and HigherGrades 5 to 7Focused skill

Curriculum path: GCSE Maths > Edexcel > Number > Percentages > Reverse percentages

Pearson Edexcel GCSE Maths number: solve reverse percentage problems using multipliers.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Reverse percentage questions give you the final amount after a percentage change.

The question usually asks for the original amount.

Do not just find the percentage of the final amount and add or subtract it. That uses the wrong starting value.

Work out what percentage of the original is left or reached.

Then divide the final amount by the multiplier.

For example, after a 20% reduction, the final value is 80% of the original, so divide by 0.8.

Key ruleReverse percentage: original = final value / multiplier.

Worked examples

After a decrease

A jacket costs 64 after a 20% reduction. Find the original price.

  1. 20% reduction leaves 80%.
  2. 80% = 0.8.
  3. Original = 64 / 0.8.

Answer: 80

After an increase

A price after a 15% increase is 92. Find the original price.

  1. 15% increase means the final price is 115% of the original.
  2. 115% = 1.15.
  3. Original = 92 / 1.15.

Answer: 80

Check the answer

A value after a 25% decrease is 60. Find the original value.

  1. 25% decrease leaves 75%.
  2. 75% = 0.75.
  3. Original = 60 / 0.75 = 80.
  4. Check: 25% of 80 is 20, and 80 - 20 = 60.

Answer: 80

Common mistakes

  • Adding 20% of the final value after a 20% reduction.
  • Using 1.2 for a 20% reduction.
  • Multiplying by the multiplier instead of dividing.
  • Not identifying whether the change was an increase or a decrease.

Quick exercise

Try these before moving to the exam-style questions.

  1. A value after a 25% decrease is 60. Find the original value.
  2. A price after a 20% increase is 96. Find the original price.
  3. A value after a 10% decrease is 45. Find the original value.
  4. A price after a 50% increase is 90. Find the original price.
  5. A value after a 5% increase is 126. Find the original value.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundation and HigherCalculator3 marks

A price after a 20% increase is 96 pounds. Find the original price.

reverse percentagespercentage increasemultipliers
Standard exam styleFoundation and HigherCalculator4 marks

A coat is sold for 72 pounds after a 40% reduction. Find the original price.

reverse percentagespercentage decreasemoney context
ChallengeHigherCalculator4 marks

A number is increased by 30% to give 91. Another student says the original number is 91 - 30% of 91. Explain why this is wrong and find the original number.

reverse percentageserror analysishigher reasoning