Appears in: Functional Skills Level 2 · GCSE foundation
Reverse percentages: how to find the original amount
A reverse percentage question gives you the amount after a percentage change and asks for the amount before it. "A jacket costs £64 after 20% off — what was the full price?" It's the percentages question that resit candidates most often get wrong, because the obvious move — add the 20% back on — gives the wrong answer.
The method
- Work out the multiplier that was applied. 20% off means the price you see is 80% of the original: multiplier 0.8. A 15% rise means you're looking at 115%: multiplier 1.15.
- Divide the amount you've been given by that multiplier. Dividing undoes the multiplying.
- Check by going forwards: apply the percentage to your answer and make sure you land on the number in the question.
Worked examples
Example 1
A jacket costs £64 after a 20% discount. What was the original price?
- After 20% off, £64 is 80% of the original. Multiplier 0.8.
- £64 ÷ 0.8 = £80.
- Check: 20% of £80 is £16, and £80 − £16 = £64.
Example 2
After a 15% pay rise, Priya earns £1,380 a month. What did she earn before?
- £1,380 is 115% of the old pay. Multiplier 1.15.
- £1,380 ÷ 1.15 = £1,200.
- Check: £1,200 × 1.15 = £1,380.
Example 3
A bill of £2,100 includes a 5% service charge. What was the bill before the charge?
- £2,100 is 105% of the original. Multiplier 1.05.
- £2,100 ÷ 1.05 = £2,000.
Where the marks go missing
- Adding the percentage back on. 20% of £64 is £12.80, and £64 + £12.80 = £76.80 — but 20% off £76.80 is £61.44, not £64. The 20% was taken from the original, which is bigger than £64.
- Using the wrong multiplier for a rise: after a 15% increase you're at 115%, so divide by 1.15, not 0.85.
Frequently asked questions
How do you work out the original price before a discount?
Divide the discounted price by (1 − the discount as a decimal). After 25% off, divide by 0.75. After 10% off, divide by 0.9.
Why can't I just add the percentage back on?
Because the percentage was taken from the original amount, which is larger than the discounted amount. Adding 20% of the smaller number gives you less than you took off.