$A$'s salary is 40% of $B$'s salary which is 25% of $C$'s salary. What percentage of $C$'s salary is $A$'s salary?

### Concept & Logic This is a chained percentage problem. By chaining the given percentage relationships into a single equation, we can find a direct correlation between the first and last variables in the chain. $$ A = \text{Percentage}_1 \times (\text{Percentage}_2 \times C) $$ ### Step-by-Step Solution * **Given:** $A$ = 40% of $B$, and $B$ = 25% of $C$. * Translate this into algebra: $A = 0.40 \times B$. * Substitute the value of $B$ into the first equation: $A = 0.40 \times (0.25 \times C)$. * Multiply the decimals: $0.40 \times 0.25 = 0.10$. * So, $A = 0.10 \times C$. * Convert the decimal back to a percentage: 0.10 = 10%. * Thus, $A$'s salary is 10% of $C$'s salary. ### Exam Strategy & Shortcut Use fractions to multiply instantly. 40% is $\frac{2}{5}$ and 25% is $\frac{1}{4}$. The combined relationship is simply the product of the fractions: $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$. Since $\frac{1}{10}$ is equal to 10%, you have your answer immediately. ### Common Pitfall A common mistake is trying to assign arbitrary numbers to $A$, $B$, and $C$ and making an arithmetic error along the way. While assigning $C=100$ works well ($B=25$, $A=10$), directly multiplying the fractional equivalents is less prone to error and much faster. ### Final Answer **Therefore, the correct answer is 10%.**