Reverse Percentages (SQA National 5 Maths): Revision Note

Working with reverse percentages

What is a reverse percentage?

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

How do I solve reverse percentage questions using percentage multipliers?

• You should think about the before quantity

  • even though it is not given in the question

• Find the percentage change as a multiplier,

  • This is the decimal equivalent of a percentage change

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

    • A percentage decrease of 7% means = 1 - 0.07 = 0.93

• Use 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

  • 

How do I solve reverse percentage questions by scaling?

• This is best seen through an example:

  • Prices in a sale have been reduced by 10%. In the sale the price of a games console is £441. What was the price of the games console before the sale?

• The new price is 100-10=90% of the original price

  • So 90% = £441

  • That means 1% = = £4.90

  • And therefore 100% = 4.90100 = £490

• The price of the games console before the sale was £490

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 2200.9 = £198 (incorrect)

  • Use before × p = after instead

    • before 1.1 = 220

    • before = = £200 (correct)