Reverse Percentages (Cambridge (CIE) O Level Maths): Revision Note

Reverse Percentages

What is a reverse percentage?

• A reverse percentage question is one where we are given the value after a percentage increase or decrease and asked to find the value before the change

How do I solve reverse percentage questions?

• You should think about the before quantity

  • even though it is not given in the question

• Find the percentage change as a multiplier, p

  • This is the decimal equivalent of a percentage change

    • A percentage increase of 4% means p = 1 + 0.04 = 1.04

    • A percentage decrease of 5% means p = 1 - 0.05 = 0.95

• Use before × p = after to write an equation

  • Get the order right: the percentage change happens to the "before", not to the "after"

• Rearrange the equation to make the "before" quantity the subject

  • Divide the "after" quantity by the multiplier, p

  • 

What is a common mistake with reverse percentage questions?

• Here is an example: a price of a mobile increases by 10% to £220

  • To find the price before, you do not apply a 10% decrease to £220

    • That would give 220 0.9 = £198 (incorrect)

  • Use before × p = after instead

    • before 1.1 = 220

    • before = = £200 (correct)

• You cannot turn a percentage increase into a decrease with reverse percentage questions