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Reverse percentages help us to work out the original price or value of an item after it has been increased or decreased in value, for example, following a price increase or a sale.

Calculating reverse percentages

Calculating reverse percentages depends on knowing that before an increase or decrease in price, an item is always worth 100% of its value, no matter what that value is. This is because 100% represents the whole amount or the full price.

Example

A shop has a sale where 20% is taken off all prices. A top is now worth £24. What price was it originally?

A common mistake is to work out 20% of £24 and add this on to £24. This will not work as 20% of £24 is not as much proportionally as 20% of the bigger, original amount.

To find the original price of the item, 100% has to be found. There are many ways to do this, but using a unitary method is a method that will always work.

80% = 24

100% of the value of the top is worth £30 which means before the sale of 20%, the top cost £30.

This answer can be tested by taking 20% off £30. If the answer is £24, then the method and answer are correct.