What will come in the place of ($z$) in the expression below: $x\%$ of $y$ is $y\%$ of ($z$)

### Concept & Formula This problem is based on the **Commutative Property of Percentages**. Because "percent" simply means dividing by $100$ and "of" denotes multiplication, the order of the variables does not change the product. $$A\% \text{ of } B = B\% \text{ of } A$$ ### Step-by-Step Solution * **Given:** * The equation: $x\% \text{ of } y = y\% \text{ of } (z)$ * (Note: We use $z$ as the unknown variable to avoid confusion with the existing $x$). * **Calculation / Deduction:** * Convert the percentages into fractions: * $\frac{x}{100} \times y = \frac{y}{100} \times z$ * Multiply both sides by $100$ to clear the denominators: * $x \times y = y \times z$ * Divide both sides by $y$ (assuming $y \neq 0$): * $x = z$ * Therefore, the unknown value is simply $x$. ### Exam Strategy & Shortcut Never do algebra for this type of question. Memorize the fundamental rule: $x\% \text{ of } y = y\% \text{ of } x$. Whenever you see an expression testing this symmetry, immediately choose the mirrored variable. ### Common Pitfall Students often get confused by the variables and try to incorporate the $100$ into the final answer, mistakenly choosing options like $100x$ or $x/100$ because they feel they haven't "used" the percentage sign in their calculation. ### Final Answer **Therefore, the correct answer is $x$.**