Working with Percentages | AQA GCSE Maths Revision Notes 2022

Reverse Percentages

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

You should think about the "before" quantity (even though it is not given in the question)
Find the percentage change as a multiplier, p (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 change happens to the "before", not to the "after"
Rearrange the equation to find the "before" quantity...
- ...by dividing the "after" quantity by the multiplier, p

A reverse percentage question involves dividing by the multiplier, p, not multiplying by it
To spot a reverse percentage question, see if you are being asked to find a quantity in the past, e.g.
Find the "old" / "original" / "before" amount ...

Jennie is now paid £31 500 per year, after having a pay rise of 5%. How much was Jennie paid before the pay rise?

The "before" amount is unknown and the "after" amount is 31 500
Find the multiplier, p (by writing 5% as a decimal and adding it to 1)

p = 1 + 0.05 = 1.05

Use "before" × p = "after" to write an equation

"before" × 1.05 = 31 500

Find "before" (by dividing both sides by 1.05)

"before" = $\frac{31 500}{1.05}$ = 30 000

She was paid £30 000 before the pay rise

Jennie was paid £30 000 before the pay rise