6.3 Reverse percentages — Learn

Prerequisites: percentage multipliers and division.

Objectives: recover an original amount after a percentage increase or decrease.

The final amount represents a percentage of the original. For a 20% decrease, the final amount is 80% of the original. Divide by 0.8 to reverse the change.

Example 1. A coat costs £72 after a 20% discount. Find its original price.

After the discount, 80% remains.

£72 is 0.8 of the original price.

£72 ÷ 0.8 = £90.

Example 2. A value after a 15% rise is 92. Find the starting value.

The increase multiplier is 1.15.

92 ÷ 1.15 = 80.

Watch out. Adding 20% of £72 does not reverse a 20% discount. The discount was calculated from the original price. Check: 20% of £90 is £18, and £90 − £18 = £72.

Progress check

A £600 balance becomes £624 after one year. What percentage of the original is £624? This prepares you to model the account over time.

You should now be able to

• identify the percentage represented by a final amount;
• divide by the correct multiplier to find an original amount;
• check a reverse percentage by applying the change again.