Why a 20% rise then a 10% cut is not a 10% rise: successive percentage changes
Successive percentage changes multiply the base rather than add.
A jacket priced at £150 is increased by 20% in a sale re-tagging, then reduced by 10% in a subsequent clearance. What is the overall percentage change on the original £150 price?
Worked solution
Correct answer: 8% increase
The principle
Successive percentage changes multiply the base rather than add.
Steps
- After the increase: 150 × 1.20 = 180.
- After the reduction: 180 × 0.90 = 162.
- Overall change = (162 - 150) / 150 = 12 / 150 = 8%.
Heuristic to carry forward
Chain successive percentage changes by multiplying the growth factors (1.20 × 0.90), never by adding or subtracting the percentages themselves.
Why each other answer is wrong
- 10% increase
- Adds the two percentages as if they applied to the same base (20% - 10% = 10%), ignoring that the second change acts on the already-increased price.
- 20% increase
- Applies only the first change (the 20% increase) and ignores the later 10% reduction.
- 12% increase
- Takes the £12 cash difference (162 - 150) as the percentage figure directly, without dividing by the original price.
Practise more questions like this one at the Wamberry practice page.