KA-0153Percentages and simple discounts
3 points, difficulty 1 of 3Level 7–8about 90sA jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
The two 20 percents are not taken from the same amount.
2The strategy
The rise is 20 percent of 80. The fall is 20 percent of the NEW price, which is bigger.
3The full solution
80 x 1.2 = 96, then 96 x 0.8 = 76.80. The jacket ends up cheaper than it started.
Solution
The reliable way
Work the two changes in order and never reuse the old base. The rise: 80 x 1.2 = 96 pounds. The fall is 20 percent of 96, not of 80, so the new price is 96 x 0.8 = 76.80 pounds. The jacket ends 3.20 pounds cheaper than it began. The transferable idea: a percentage is always a percentage OF something, and after the first change that something has moved.
The elegant way
Multiplying by 1.2 and then by 0.8 is multiplying by 0.96, so any starting price ends 4 percent lower.
Why this is on the test: The belief that equal percentage rises and falls cancel is one of the most common errors on the paper.