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**Percentages — formulas used here.** - Definition. $x\%$ means $\tfrac{x}{100}$. - Increase consumption. If price rises by $R\%$ and spending must stay constant, consumption falls by $\tfrac{R}{100+R} \times 100\%$. - Decrease consumption. If price falls by $R\%$ and spending must stay constant, consumption rises by $\tfrac{R}{100-R} \times 100\%$. - Growth. A population $P$ growing at $R\%$ a year becomes $P(1 + \tfrac{R}{100})^n$ after $n$ years, and was $P / (1 + \tfrac{R}{100})^n$, $n$ years ago. - Depreciation. A value $V$ depreciating at $R\%$ a year becomes $V(1 - \tfrac{R}{100})^n$ after $n$ years. - Reciprocal comparisons. If A is $R\%$ more than B, then B is $\tfrac{R}{100+R} \times 100\%$ less than A. If A is $R\%$ less than B, then B is $\tfrac{R}{100-R} \times 100\%$ more than A. **Question.** If A's salary is $25\%$ more than B's salary, by what percent is B's salary less than A's?

A$15\%$
B$20\%$
C$25\%$
D$30\%$
Answer & Solution
Correct answer: B. $20\%$
**Principle.** If A is $R\%$ more than B, then B is $\tfrac{R}{100+R} \times 100\%$ less than A — the base of comparison flips. **Plug in.** $\tfrac{25}{100 + 25} \times 100\% = \tfrac{25}{125} \times 100\% = 20\%$. **Why option C is wrong.** The most tempting wrong answer is $25\%$ — symmetry says they should be the same. But the *base* has changed: $25\%$ of B is not $25\%$ of A, because A is larger. The percent has to drop to compensate.
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