Percentages • Topic 4 of 8

Successive Percentages

When percentage changes are applied one after another, multiply their factors rather than adding the percentages. A 20% rise followed by a 10% fall is × 1.20 × 0.90 = × 1.08, a net 8% increase — not 10%. Each change acts on the result of the previous one, so the base shifts each time. This is why a 50% loss needs a 100% gain to recover. On the SAT, successive percentages appear in repeated discounts, compound growth and "two changes in a row" problems; setting up the product of factors is faster and less error-prone than working step by step.

✅ Solved examples

1. A price is increased 10% then decreased 10%. Net change?
1.10 × 0.90 = 0.99, a 1% decrease overall.
2. 100 is increased 20% then 30%. Final value?
100 × 1.20 × 1.30 = 156.
3. A $200 item is discounted 25% then a further 20%. Final price?
200 × 0.75 × 0.80 = $120.
4. A quantity drops 50% then rises 50%. Net change?
0.50 × 1.50 = 0.75, a 25% decrease overall.

✏️ Practice — try these, take hints as needed

1. A value is increased 25% then decreased 20%. Net change?
Multiply 1.25 × 0.80.
= 1.00.
Interpret the factor.
No net change (factor 1.00).
2. 50 is increased 10% then 20%. Final value?
50 × 1.10 × 1.20.
50 × 1.32.
Compute.
66.
3. A $400 item is discounted 10% then 10%. Final price?
400 × 0.90 × 0.90.
400 × 0.81.
Compute.
$324.
4. A price rises 50% then falls 20%. Net percent change?
1.50 × 0.80 = 1.20.
Factor 1.20 means +20%.
State it.
20% increase.
5. 200 is decreased 25% then increased 40%. Final value?
200 × 0.75 × 1.40.
200 × 1.05.
Compute.
210.

📝 Topic test — 8 questions

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