The idea

Reverse percentages

How to find the original amount before a percentage change, and why you must divide by the multiplier rather than apply the percentage to the new amount.

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Ratio, proportion & rates of change · Percentages & growth

Reverse percentages

How to find the original amount before a percentage change, and why you must divide by the multiplier rather than apply the percentage to the new amount.

Why it works

The percentage belongs to the number you don't know

A reverse percentage question gives you the amount after a change and asks for the amount before it. The whole difficulty is a single trap: the percentage in the question is a percentage of the original, which is exactly the number you don't know yet — so you must not apply it to the number you do know.

Think of the forward direction first. If the original is

x

and it goes up by

20\%

, the multiplier is

1.2

and the new amount is

1.2 \times x = \text{new amount}.

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The rest of the explanation, plus 2 worked examples you step through move by move.

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