A percentage increase or decrease is always measured against the amount you started from. To find the percentage change, work out the change first, then compare it with the ORIGINAL amount and multiply by 100. To apply a change, an increase of 15% makes the new amount 115% of the old one and a decrease of 15% leaves 85% of it. When a price changes twice, the second percentage is of the amount after the first change, not of the original — which is why a 20% rise followed by a 25% fall is not a 5% fall.
Worked example
Problem The price of a television set was $800. In January the price was increased by 20%. In June the new price was decreased by 25%. Find the price in June, and the overall percentage change.
Take the original price $800 as 100%.
After rising by 20% the price is 120% of $800: 6/5 × 800 = 960, so the January price is $960.
Watch out The June change is worked out on the January price of $960, NOT on the original $800. The whole has moved.
After falling by 25% the price is 75% of $960: 3/4 × 960 = 720, so the June price is $720.
Compared with the original, the price has fallen by $800 − $720 = $80. As a percentage of the ORIGINAL price: 80/800 = 1/10, and 1/10 × 100 = 10, so the overall decrease is 10%.
Tip You cannot just add and subtract the two percentages — they are percentages of different amounts.