KA-0065Percentages and simple discounts
4 points, difficulty 2 of 3Level 5–6about 90sA price goes up by 20%, then down by 20%. Compared with the original price, the final price is:
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Start from 100 and follow it through.
2The strategy
Pick a convenient starting price and apply the two changes in order. The second percentage is taken of the new price, not the original one, which is the whole point.
3The full solution
Start at 100. Up 20% gives 120. Down 20% of 120 is a fall of 24, giving 96 — which is 4% below 100.
Solution
The reliable way
Take a starting price of 100. A 20% rise gives 120. A 20% fall is now 20% of 120, which is 24, so the price becomes 96. That is 4 below 100, or 4% lower. The transferable idea: name what the percentage is a percentage of, every single time — the second one is not of the original price.
The elegant way
Multiplying by 1.2 and then by 0.8 gives 0.96 whatever the starting price, so the order does not matter and the loss is always 4%.
Why this is on the test: The belief that a rise and a fall of the same percentage cancel is one of the most durable misconceptions in the whole syllabus.