$x$% of $y$ is $y$% of

### Concept & Logic This question tests the commutative property of multiplication as it applies to percentages. The fundamental rule of percentages is that $A\%$ of $B$ is exactly equal to $B\%$ of $A$. $$ \frac{A}{100} \times B = \frac{B}{100} \times A $$ ### Step-by-Step Solution * Let the unknown value be $k$. * The question states: $x\%$ of $y = y\%$ of $k$. * Translate this into an algebraic equation: $$ \left(\frac{x}{100}\right) \times y = \left(\frac{y}{100}\right) \times k $$ * Simplify the left side: $$ \frac{xy}{100} = \frac{yk}{100} $$ * Multiply both sides by $100$ to clear the denominators: $$ xy = yk $$ * Assuming $y$ is not zero, divide both sides by $y$: $$ x = k $$ * Therefore, the missing value is $x$. ### Exam Strategy & Shortcut **Memorize the Rule:** You should never need to calculate this. Memorize the identity: **$x\%$ of $y = y\%$ of $x$**. For example, $8\%$ of $50$ is hard to calculate in your head, but $50\%$ of $8$ is instantly $4$. Recognizing this property allows you to select option (a) in less than two seconds. ### Common Pitfall Students who rely too heavily on algebra might overcomplicate this and mistakenly select $\frac{x}{100}$ or $100x$ by fumbling the fractions during transposition. Always look for fundamental properties before doing raw calculations. ### Final Answer **Therefore, the correct answer is $x$.**