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Percentage practice: increase, decrease and reverse

To find a reverse percentage, treat the final amount as its percentage of the original and divide by the multiplier. A coat costing 48 pounds after 20 percent off is 80 percent of the original, so divide 48 by 0.8 to get the original price of 60 pounds.

Percentages appear on every maths paper and in daily life, from sale prices to interest rates. The hardest version at GCSE is the reverse percentage, where you are given the final amount and asked for the original.

Year 8Year 9GCSE FoundationGCSE Higher

The method, step by step

  1. Decide the direction. Are you finding a percentage of something, or working backwards to the original?
  2. Use a multiplier. A 20% increase is ×1.2, a 20% decrease is ×0.8.
  3. Reverse by dividing. If the final amount came from a decrease, divide by the multiplier rather than adding the percentage back.
  4. Sense-check. A reversed original should always be larger than a discounted price.

Worked example

A coat costs £48 after a 20% discount. What was the original price?
£48 represents 80% of the original, not 100%.
The multiplier for a 20% decrease is 0.8.
Divide rather than add: 48 ÷ 0.8 = 60.
The original price was £60

Common mistakes

Adding 20% back onto £48, which gives £57.60 and is wrong. The percentage was taken from the larger original, not the smaller sale price.

Treating a 20% rise followed by a 20% fall as returning to the start. It does not.

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FractionsRatioSolving equationsGCSE maths