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Reverse Percentages

GCSELevel 6-7Cambridge iGCSE

Reverse Percentages Revision

Reverse Percentages

Finding the original value before a percentage change has been applied is called a reverse percentage.

Once you are able to recognise it is a reverse percentage question, the method is very simple.

Method 1: Calculating 1\%

  1. Write the amount given as a percentage of the original amount.
  2. Find 1\% of the original amount by dividing by this value
  3. Multiply by \textcolor{#aa57ff}{100}


The price of a pair of trainers has been decreased by 20\%.

If its new price is £60.80, work out its original price.


  1. The trainers have been decreased by 20\%, so £60.80 represents \textcolor{#10a6f3}{80\%} of its original value.
  2. Divide by 80 to find 1\% of the original price.
  3. Multiply by \textcolor{#10a6f3}{100}

£60.80 \div80=£0.76 (1\%)

£0.76\times 100=\textcolor{#10a6f3}{£76} (original price) 

Level 6-7GCSECambridge iGCSE

Method 2: Using Decimals

If you are comfortable with the method described above, you may find it easier to skip step 2 and 3.

This can be done by converting the percentage found in step 1 into a decimal and dividing by this value instead.


The value of a painting has increased by 30\% over the course of a year to £858.

Work out the value of the painting a year ago.

  1. £858 represents \textcolor{#10a6f3}{130\%} of the original value of the painting.
  2. Convert this percentage to a decimal: 130\%=\textcolor{#10a6f3}{1.3}
  3. Divide by 1.3

£858 \div 1.3=\textcolor{#10a6f3}{£660}

Level 6-7GCSECambridge iGCSE


As part of a black Friday deal a laptop has been reduced by \textcolor{#10a6f3}{28\%} to £547.20.

Calculate the original price of the laptop before the discount.

[2 marks]

First find what percentage of the original price £547.20 is.


Convert to a decimal:

72\div 100=\textcolor{#10a6f3}{0.72}

Divide the new price by this decimal:

£547.20 \div 0.72=\textcolor{#10a6f3}{£760}

Level 6-7GCSECambridge iGCSE

Reverse Percentages Example Questions

£5880 is 70\% of the original value of the car.

Original value =£5880\div 0.7=£8400 

55319 represents 103.4\% of the population of the town in 2020.

Population of the town in 2020 =55319 \div 1.034=53500

27 goals represents 30\% of the team’s total goals.

Total number of goals =27\div 0.3=90

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