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Reverse percentages involve working backwards through a calculation to find the original amount (before a percentage change). It involves finding the original amount when the reduced (or increased) amount is known. The % decrease (or increase) must also be known.

Tips to answer reverse percentage questions.

• Read the question carefully. If you are given an amount which has already been reduced or increased, then it probably is a reverse percentage question.

• Look out for phrases like ‘original price/value’ or ‘value before’ reduction/increase.

• Make sure that your answer makes sense. It should be bigger if the value has been reduced/decreased and smaller if the value has been increased.

Example

In a sale, the price of a coat is reduced by 15% and now is on sale for £76.50.
What was the original price of the coat?

Solution:

The sale price and the % reduction have been given so it is a reverse % question.

The sale price is 85% of the original cost.

• 85% = £76.50

• 1% = 76.50 ÷ 85 = 0.9

• 100% = 0.9 x 100.

• = 90

Check:
85% of £90 = 90 x 0.85 = £76.50 ✓

Answer:

The original price was £90.

Example

After a price increase of 10% a games console costs £537.90.
What was the cost before the increase?

Solution:

Increased price is 110% of original price.

• 110% = £537.90

• 1% = 4.89

• 100% = 4.89 x 100

• = 489

Check:
100% of £489 = 489 x 1.1 = £537.90 ✓

Answer:

The games console cost £489 before the price increase.