A coat costs £48 after 20% off. What was it before?
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The tempting mistake
Adding 20% back to £48 gives £57.60, which is wrong. The 20% was of the larger original, not of £48.
Divide by the multiplier
£48 is 80% of the original, so the original is 48 ÷ 0.8 = £60.
Check forwards
20% of 60 is 12, and 60 − 12 = 48. It fits.
Undo a percent change by dividing
If a 20% discount left a price of £48, then £48 is 80% of the original, so the original is 48 ÷ 0.8 = £60. You multiplied to apply the change, so you divide to undo it.
The tempting wrong answer
Adding 20% back to £48 gives £57.60, not £60, because the 20% is now being taken of the smaller number. Percent changes are not undone by applying the opposite percentage — they are undone by dividing by the multiplier.
Removing tax works the same way
A price of £60 including 20% tax had a pre-tax price of 60 ÷ 1.2 = £50. Anyone who deals with invoices does this calculation constantly, and the wrong method — taking 20% off £60 — gives £48, which is out by £2.
Check by applying the change forwards
Take your answer of £60 and apply the 20% discount: 60 × 0.8 = 48, matching the given price. Working forwards from your answer is the natural check for any backwards problem.
Step 2: Try It Yourself
Tap and try it out.
paid and discount
48
12
the original
?
The hatched bar is the piece the story is asking for.
Step 3: Watch an Example
One step at a time.
Watch Leo Undo an Increase
A price is £60 after a 20% rise.
- Step 1
A 20% rise multiplied the original by 1.2.
Step 4: Your Turn
Practice makes it stick.
The Sale Tag
Problem 1 of 2
£40 after 20% off. What was the original, in pounds?
The Rise
Problem 2 of 2
£110 after a 10% rise. What was the original, in pounds?
Work Backwards
1 of 4
£90 after 10% off. Original in pounds?
2 of 4
£75 after 25% off. Original in pounds?
3 of 4
£120 after a 20% rise. Original in pounds?
4 of 4
Is adding 20% back to a discounted price correct? Answer 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
£64 after 20% off. Original in pounds?
What You Learned
- A percent change multiplies the original by a fixed multiplier.
- To go backwards, divide by that multiplier.
- Adding the percent back on is a different, and wrong, calculation.