($x$% of $y + y$% of $x$) =

### Concept & Formula This problem elegantly tests the commutative property of multiplication within percentages. The rule $A$% of $B = B$% of $A$ is a core shortcut in quantitative aptitude. When you add two mathematically identical quantities together, you simply double the quantity. $$ a\% \text{ of } b = \frac{ab}{100} $$ ### Step-by-Step Solution * **Given:** Expression: ($x$% of $y + y$% of $x$) * **Calculation:** Convert both percentage terms into standard algebraic fractions to reveal their underlying structure: $$ \text{Term 1} = \frac{x}{100} \times y = \frac{xy}{100} $$ $$ \text{Term 2} = \frac{y}{100} \times x = \frac{xy}{100} $$ Add the two identical terms together: $$ \frac{xy}{100} + \frac{xy}{100} = \frac{2xy}{100} $$ Now, convert this combined fraction back into a percentage format to match the given options. The fraction $\frac{2}{100}$ represents exactly 2%: $$ \frac{2}{100} \times xy = 2\% \text{ of } xy $$ ### Exam Strategy & Shortcut Recognize immediately that "$x$% of $y$" and "$y$% of $x$" are the exact same mathematical entity due to the commutative property. It's like adding one Apple to another Apple to get 2 Apples. Therefore, $x$% of $y$ + $y$% of $x$ = 2 times ($x$% of $y$). This directly translates to 2% of $xy$. You can solve this by pure inspection without writing a single fraction down. ### Common Pitfall Students sometimes overcomplicate this by trying to arbitrarily factor out variables or convert things into complex algebraic structures, completely missing that the two terms are identical and simply need to be added together algebraically. ### Final Answer Therefore, the correct answer is **2% of $xy$**.