GCSE MATHS • HIGHER TIER
Reverse Percentages Made Simple
Work backwards from a final value to find the original amount using percentage multipliers.
Clear method
Exam practice
Worked proofs
Reverse Percentages in Four Moves
1
Identify
Identify whether the final value came from a percentage increase or decrease.
2
Convert
Convert the percentage change into the correct multiplier.
3
Divide
Divide the final amount by the multiplier to work backwards.
4
Check
Apply the percentage change to your original amount and confirm the final value.
What You’ll Learn
Understand Arc Length
Understand that an arc is part of a circle’s circumference.
Use Circle Vocabulary
Recognise radius, diameter, circumference, arc, sector and central angle.
Apply the Formula
Calculate arc length using the angle as a fraction of 360°.
Exact and Decimal Answers
Give answers in terms of π or as decimal approximations.
Key Rules
Identify whether the value increased or decreased.
For an increase, use :
Multiplier = 1 + percentage ÷ 10.
For a decrease, use :
Multiplier = 1 − percentage ÷ 100.
To find the original amount :
Original amount = Final amount ÷ Multiplier.
Worked Proof: Reverse Percentages
Step-by-Step Method
Reverse percentages are easiest using multipliers
Increase by 10% → Multiplier = 1.10
Decrease by 20% → Multiplier = 0.80
To work backwards: Final Amount ÷ Multiplier
More Worked Examples
1
A coat costs £80 after a 20% discount.
20% discount means 80% remains.
Multiplier = 0.80
£80 ÷ 0.80 = £100
£80 ÷ 0.80 = £100
2
A salary increases by 10% and becomes £33,000.
Multiplier = 1.10
£33,000 ÷ 1.10 = £30,000
3
A bike is sold for £540 after a 10% discount.
90% remains.
Multiplier = 0.90
£540 ÷ 0.90 = £600
£540 ÷ 0.90 = £600
4
A population increases by 25% to 10,000.
Multiplier = 1.25
10,000 ÷ 1.25 = 8,000
- Common GCSE Mistakes
- Subtracting the percentage instead of using a multiplier.
- Multiplying instead of dividing when working backwards.
- Using the wrong percentage multiplier.
- Confusing increase and decrease questions.
- Exam Tips
- Identify whether the change is an increase or a decrease before choosing a multiplier.
- For a decrease, find the percentage that remains.
- To reverse a percentage change, divide the final amount by the multiplier.
- Do not simply add or subtract the stated percentage from the final value.
- Write the multiplier clearly before using your calculator.
- Check your answer by applying the original percentage change again.
Skills Used in Reverse Percentages
Percentages
Percentage Multipliers
Division
Money
Discounts
Percentage Increase
Percentage Decrease
VAT
Algebraic Thinking
Problem Solving
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Reverse Percentages Tutorial
Step-by-step walkthroughs of Reverse Percentages with clear methods and exam tips.
Frequently Asked Questions
Reverse percentages involve working backwards to find an original amount after a percentage increase or decrease has already been applied.
Convert the percentage change into a multiplier and divide the final amount by that multiplier.
A 20% discount leaves 80%, so use a multiplier of 0.80 and divide the final amount by 0.80.
Use the multiplier 1.10 and divide the final amount by 1.10.
Yes. The source gives an example where a price including 20% VAT uses a multiplier of 1.20.
The percentage change was originally applied by multiplying, so working backwards requires division by the multiplier.