Reverse Percentages (Edexcel IGCSE Maths A (Modular))

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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
- 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

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 $\times$ 0.9 = £198 (incorrect)
- Use before × p = after instead
  - before $\times$ 1.1 = 220
  - before = $\frac{220}{1.1}$ = £200 (correct)
You cannot turn a percentage increase into a decrease with reverse percentage questions

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 ...

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)

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

She was paid £30 000 before the pay rise

Jennie was paid £30 000 per year before the pay rise

the (exam) results speak for themselves:

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