Percentages • Topic 3 of 5

Successive Percentage Change

When two percentage changes happen one after another you cannot just add them. The exact net for a% followed by b% is a + b + ab/100, with increases positive and decreases negative. So +20% then +30% gives 20 + 30 + (20×30)/100 = 56%, not 50%. For three or more changes, chain the decimal multipliers: 1.2 × 0.9 × 1.1. This single idea powers a large family of GRE questions — population or investment growth over two years, two successive discounts, and "raise then cut" traps. On test day the multiplier chain done mentally is almost always faster than the formula, and it is far less error-prone than trying to add percentages.

✅ Solved examples

1. A rent rises 10% one year and 20% the next. Net increase?
Net = 10 + 20 + (10×20)/100 = 32%.
2. Two successive discounts of 20% and 10% equal what single discount?
Net = −20 − 10 + (−20 × −10)/100 = −28% ⇒ a single 28% discount.
3. A value increases 50% then decreases 50%. Net change?
50 − 50 + (50 × −50)/100 = −25% ⇒ a 25% net decrease.
4. A population grows 10%, 20%, 30% over three years. Net growth?
1.1 × 1.2 × 1.3 = 1.716 ⇒ 71.6% growth.

✏️ Practice — try these, take hints as needed

1. Net effect of +25% then +25%?
a + b + ab/100.
25 + 25 + 625/100.
50 + 6.25.
+56.25%
2. Successive discounts of 10% and 10% equal what single discount?
Both negative.
−10 −10 + (100/100).
−20 + 1.
19%
3. A stock rises 20% then falls 20%. Net change?
× 1.2 × 0.8.
= 0.96.
Loss of 4%.
−4%
4. Salary cut 20% then raised 25% — back to normal?
× 0.8 × 1.25.
= 1.00.
Yes.
0% net (unchanged)
5. A value rises 10% each year for 2 years. Net?
1.1 × 1.1.
= 1.21.
Add the cross term.
+21%

📝 Topic test — 8 questions

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