Edexcel International GCSE Mathematics A · 4MA1
Reverse percentages
A reverse percentage problem gives the amount after a change and asks for the original. The final amount represents a new percentage of the original: for example, a 20% reduction leaves 80%. Work backwards by dividing by that multiplier.
Key method
Original = final ÷ multiplier. Label the original amount as 100% before choosing the multiplier; this prevents taking a percentage of the wrong amount.
Worked example
A jacket costs 68 after a 15% discount. What was its original price?
- After a 15% discount, the sale price is 85% of the original.
- Write 0.85 × original = 68.
- Divide by 0.85: original = 80.
Answer and interpretation
The original price was 80.
Common mistake
Adding 15% of 68 does not undo a 15% discount on the original amount.
Practise independently
A population is 1260 after a 5% increase. Find the starting population.
Check your answer
1260 ÷ 1.05 = 1200.
Syllabus connection
This lesson develops reverse percentages within the number area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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