FRACTIONS, DECIMALS AND PERCENTAGES

Reverse Percentages

Learn the reliable method for reverse percentages, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A percentage is a number of parts out of 100. Fractions, decimals and percentages are different ways to show the same proportion.

Picture itConnect parts out of 100
Stationery and UK money arranged as a real-life shopping problem
2 · THE METHOD

Follow these steps

  1. Identify what percentage the given final value represents.
  2. Scale that value to the percentage required.
  3. Check whether the answer should be smaller or larger than the starting amount.
original = final ÷ remaining percentage × 100
3 · WORKED EXAMPLES

See the method in action

Example 1

A shop sells 4 identical items for £1020 altogether after reducing each price by 25%. What was the original price of one item?

  1. Divide the bill by 4: £1020 ÷ 4 = £255.
  2. Reverse the reduction: £255 ÷ 0.75 = £340.
Answer: £340.00
Example 2

A shop reduces a price by 25%, then reduces the new price by 20%. The final price is £420.00. What was the original price?

  1. Reverse the second reduction: £420.00 ÷ 0.8 = £525.
  2. Reverse the first: £525 ÷ 0.75 = £700.
Answer: £700.00
4 · ELEVENSPRINT TIP

A useful shortcut

For reverse percentages, divide by the percentage represented—not the percentage change.

5 · COMMON MISTAKES

Watch out for these

Using the final value as 100%

In a reverse problem, the final value represents the percentage left.

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.