Find the value of x% of y + y% of x

Options

A. 3% of xy
B. 2% of xy
C. 5% of xy
D. 4% of xy

Answer

To solve the problem of finding the value of \( x\% \) of \( y + y\% \) of \( x \), we can follow these steps:

### Step 1: Understand the expression
We need to evaluate the expression \( x\% \) of \( y + y\% \) of \( x \).

### Step 2: Convert percentages to fractions
Recall that \( x\% \) means \( \frac{x}{100} \). Therefore:
- \( x\% \) of \( y \) can be written as \( \frac{x}{100} \times y \).
- \( y\% \) of \( x \) can be written as \( \frac{y}{100} \times x \).

### Step 3: Write the expression using fractions
Now, we can rewrite the expression:
\[ x\% \text{ of } y + y\% \text{ of } x = \frac{x}{100} \times y + \frac{y}{100} \times x \]

### Step 4: Combine the terms
Both terms \( \frac{x}{100} \times y \) and \( \frac{y}{100} \times x \) are similar, so we can combine them:
\[ = \frac{xy}{100} + \frac{xy}{100} \]
\[ = 2 \times \frac{xy}{100} \]

### Step 5: Simplify the expression
Now, we can simplify:
\[ = \frac{2xy}{100} \]
This can also be expressed as:
\[ = \frac{2}{100} \times xy = 2\% \text{ of } xy \]

### Conclusion
Thus, the value of \( x\% \) of \( y + y\% \) of \( x \) is \( 2\% \) of \( xy \).

### Answer
The correct option is **b) 2% of xy**.

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