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- EDEXCEL GCSE
- AQA GCSE
- OCR GCSE
- EDUQAS GCSE

**Reverse percentages** are used to find the original amount before a percentage increase or decrease. This is helpful when you know the final amount after the change and need to determine the original value.

If a price after a 20% increase is 120, think about how we would have found out this answer if we knew the original price.

\[\text{original } \times \text{ multiplier } = \text{ final}\]

\[\text{original } \times 1.2 = \text{ final}\]

But we have the final amount, not the original.

\[\text{original } \times 1.2 = 120\]

To find the original price we need to do the **inverse** (or opposite) of \(\times 1.2\).

\[120 \div 1.2 = \text{original }\]

\[120 \div 1.2 = 100\]

We can use this after a percentage increase or decrease. We can even apply this to repeated percentage changes.

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