Reverse-Percentages Aqa Foundation

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Exam code:8300

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
- $Before equals After over Multiplier$

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 $cross times$ 0.9 = £198 (incorrect)
- Use before × p = after instead
  - before $cross times$ 1.1 = 220
  - before = $fraction numerator 220 over denominator 1.1 end fraction$ = £200 (correct)
You cannot turn a percentage increase into a decrease with reverse percentage questions

Examiner Tips and Tricks

To spot a reverse percentage question, see if you are being asked to find a quantity in the past
- Find the old / original / before amount …

Worked Example

Jennie has been working for a company for the last ten years.

She receives a pay rise of 5%.

Her new salary is £31 500 per year.

Find her salary before the pay rise.

Use “before” × p = “after” to write an equation

The “before” amount is unknown and the “after” amount is 31 500

“before” × 1.05 = 31 500

Find the multiplier, p (by writing 5% as a decimal and adding it to 1)

p = 1 + 0.05 = 1.05

Find the value of “before” (by dividing both sides by 1.05)

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Maths Gcse Aqa Foundation

Reverse-Percentages Aqa Foundation