Reverse Percentages (Cambridge (CIE) O Level Maths): Revision Note
Exam code: 4024
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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
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)
"before" = = 30 000
She was paid £30 000 before the pay rise
Jennie was paid £30 000 per year before the pay rise
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