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Successive percentage changes

2026-10-05Percentage, Rate & Ratio Ms Lam

Combine successive percentage changes by multiplying multipliers — never by adding the percentages.

Key formulas

Final = Original \times m1 \times m2 \times …

\text{Overall multiplier} = \text{product of stage multipliers}

Why you multiply multipliers

Each percentage change acts on the result of the previous stage. If Stage 1 uses m1 and Stage 2 uses m2, the overall multiplier is m1 × m2. Adding the percentage rates is wrong except in the special case of tiny rates used as rough estimates.

Mixed increase and decrease

A shop marks up 30% then offers 10% off: overall multiplier = 1.3 × 0.9 = 1.17, so a 17% overall increase on the cost price — not a 20% increase.

Finding an equivalent single change

Compute the product of multipliers, then convert (overall multiplier − 1) × 100% into a single percentage increase, or (1 − overall multiplier) × 100% into a single percentage decrease.

Exam habit

List each multiplier on its own line, multiply, then interpret the final multiplier in words.

Worked example

Up then down

Problem. A value increases by 20% then decreases by 20%. Find the overall percentage change.

Solution. Multipliers 1.2 and 0.8. Product = 0.96. Overall change = 4% decrease.

Review quiz

1 / 4

Rise 10% then 10%. Overall multiplier?

Practice questions

A salary rises 8% then 5%. Find the overall percentage increase.
A price rises 25% then falls 20%. Find the overall percentage change.
After two equal percentage increases the value is 1.44 times the original. Find each increase.