#7
Top 50 Mistake
Finding percentage of final amount for reverse problems
"The Backwards Blunder"
The Mistake in Action
After a 20% discount, a jacket costs £48. Find the original price.
Wrong: $20\%$ of $48 = £9.60$ Original = $48 + 9.60 = £57.60$
Why It Happens
Students find 20% of the sale price and add it back, but £48 is not 100% — it's already reduced!
The Fix
After a 20% discount, the price represents 80% of the original (100% - 20% = 80%).
Correct method:
- £48 = 80% of original
- 1% of original = $48 \div 80 = £0.60$
- 100% (original) = $0.60 \times 100 = £60$
Or use the multiplier:
- Multiplier for 20% decrease = 0.80
- Original = $48 \div 0.80 = £60$
Check: $60 \times 0.80 = £48$ ✓
Spot the Mistake
Can you identify where this student went wrong?
After a 20% discount, a jacket costs £48. Find the original price.
20% of 48 = £9.60
Original = $48 + 9.60 = £57.60$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: