Percentage discounts — what you actually pay
How do you work out a percentage discount?
A "30% off" sign in a shop window looks simple, but there are two separate questions here: how much money you save, and how much you actually pay. And sometimes there is a real trap — when two discounts come one after the other, you cannot simply add the percentages.
Worked examples, step by step
A shirt costs £120 and there is 25% off. How much do you pay?
- First find the size of the discount: (120 × 25) ÷ 100 = £30
- Subtract from the original price: 120 − 30 = 90
- Or directly: 120 × (100 − 25) ÷ 100 = 120 × 0.75 = 90
- Answer: you pay £90
A £200 item has 20% off, and then a further 10% off the already reduced price. Is the total discount 30%?
- After 20% off: 200 × 0.8 = £160
- After a further 10% off 160: 160 × 0.9 = £144
- The total discount: 200 − 144 = £56
- 56 out of 200 is (56 ÷ 200) × 100 = 28%
- Answer: the total discount is 28%, not 30% — because the second discount is worked out on a price that has already been reduced, not on the original price
A price drops from £250 to £200. What percentage discount is that?
- The discount in pounds: 250 − 200 = 50
- The percentage: (50 ÷ 250) × 100
- 50 ÷ 250 = 0.2
- 0.2 × 100 = 20
- Answer: it is a 20% discount
After 40% off, an item costs £90. What was the original price?
- After 40% off, 60% of the original price remains
- 60% of the original price = £90
- Original price = (90 × 100) ÷ 60
- 90 × 100 = 9000, and 9000 ÷ 60 = 150
- Answer: the original price was £150
Now try it yourself
Frequently asked questions
How do you work out what you pay after a discount?
Price after discount = original price × (100 − discount %) ÷ 100. For example an £80 item with 25% off: 80 × 75 ÷ 100 = £60.
Are two discounts of 20% and 10% the same as 30% off?
No — that is a common mistake. The second discount is worked out on the price already reduced by the first, not on the original price. So the total discount is always smaller than the simple sum of the percentages: 20% then 10% comes to 28% off in total, not 30%.
How do you find the percentage discount when you only know the two prices?
Subtract the new price from the original to get the discount in pounds, then divide by the original price and multiply by 100: (difference ÷ original price) × 100.
Does the order of the discounts matter?
No — 20% then 10% gives exactly the same final price as 10% then 20%, because multiplying by 0.8 and 0.9 gives the same result in either order. But in both cases it is less than 30% off, which is what shops rely on when they advertise "up to 30% off".
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: