Percentage, Profit & Loss • Topic 2 of 4

Percentage Change

A percentage increase then a decrease (or vice versa) does NOT cancel out. If a value rises by a% and then falls by a%, the net change is a loss of (a^2/100)%. Successive changes multiply factors: a 20% rise and a 10% rise give x 1.2 x 1.1 = x 1.32, a net 32% rise. For population/price problems, chain the multipliers.

✅ Solved examples

1. A salary is increased by 20% then decreased by 20%. Net change?
Net = -(20 x 20)/100 = -4%, i.e. a 4% decrease.
2. A price rises 10% then rises another 20%. Overall rise?
1.10 x 1.20 = 1.32, so 32% rise.
3. If length increases 25% and breadth decreases 20%, change in area?
1.25 x 0.80 = 1.00, no change (0%).
4. A number is increased by 50% and the result decreased by 40%. Net?
1.5 x 0.6 = 0.9, a 10% decrease.

✏️ Practice — try these, take hints as needed

1. Increase 30% then decrease 30%. Net change?
Use -a^2/100.
900/100.
—
9% decrease
2. Two successive rises of 10% and 10%?
1.1 x 1.1.
1.21.
—
21% rise
3. Side of a square increased 20%. Area change?
Area factor = 1.2^2.
1.44.
—
44% increase
4. Price up 25%, then down 20%?
1.25 x 0.80.
1.00.
—
No change
5. A rises 40%, then falls 50%?
1.4 x 0.5.
0.7.
—
30% decrease

📝 Topic test — 8 questions

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