Successive percentage changes: the +10% then −10% trap

The classic trap

An item costs $100.

• Increase 10%: new price $110.
• Decrease 10%: new price 110 × 0.9 = **$99**, not$100.

You lost 1% along the way! Two opposite changes never cancel out.

The tool: the multiplier

An increase of $+t\%$ corresponds to a multiplier of $1 + t/100$. A decrease of $-t\%$ corresponds to a multiplier of $1 - t/100$.

To chain two changes, multiply the multipliers: $\text{Total multiplier} = M_1 \times M_2$

Example: +20% then −15%

$M = 1.20 \times 0.85 = 1.02$

That’s a +2% total change.

Mental trick for two small changes

For $\pm a\%$ followed by $\pm b\%$ with small $a, b$: $\text{Total} \approx (a + b) \% + (a \times b / 100) \%$

Example: +10% then −10% → $(10 - 10) + (10 \times (-10) / 100) = -1$%. ✓

Mistake to NEVER make

You never add percentages!

+30% then +20% ≠ +50%.

Real answer: $1.30 \times 1.20 = 1.56$ → +56%.

?À toi de jouer

An item drops 40% then rises 40%. What is the total change?

A.−16% (it's 84% of original price)B.0%C.+16%D.−80%

Valider