Reverse Percentages

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}

Example:

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) 

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.

Example:

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}