Percentages • Topic 3 of 5

Successive Percentage Change

When two percentage changes happen one after another, you cannot just add them. The exact net change for a% followed by b% is a + b + ab/100, where increases are positive and decreases negative. For example +20% then +30% gives 20 + 30 + (20×30)/100 = 56%, not 50%. For three changes, apply the two-change formula twice, or simply multiply the decimal multipliers. This single formula powers a huge family of CAT questions: population growth over two years, two successive discounts, price-then-quantity changes, and "increase then decrease" traps. The fastest method in the exam is almost always the multiplier chain (e.g. 1.2 × 0.9 × 1.1) done mentally.

✅ Solved examples

1. A salary increases 10% in year 1 and 20% in year 2. Net increase?
Net = 10 + 20 + (10×20)/100 = 32%.
2. Two successive discounts of 20% and 10% are equal to what single discount?
Net = −20 −10 + (−20×−10)/100 = −28% ⇒ a single discount of 28%.
3. A value increases 50% then decreases 50%. Net change?
50 − 50 + (50×−50)/100 = −25% ⇒ 25% net decrease.
4. 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. Single discount equal to 10% and 20% successive?
Both negative.
−10 −20 + 200/100.
−30 + 2.
28%
3. A number is increased 20% then decreased 20%. Net?
20 − 20 + (20×−20)/100.
0 − 4.
Net decrease.
4% decrease
4. Length +10%, breadth +20%. Area changes by?
Area = L×B, so multiply.
1.1 × 1.2.
= 1.32.
+32%
5. Side of a square increased 30%. Area increases by?
+30% then +30%.
30 + 30 + 900/100.
60 + 9.
+69%

📝 Topic test — 8 questions

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