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 break it down into steps.

### Step 1: Understand the Percentages
First, we need to convert the percentages into decimal form.
- \( x\% \) can be written as \( \frac{x}{100} \).
- \( y\% \) can be written as \( \frac{y}{100} \).

### Step 2: Calculate \( x\% \) of \( y \)
Now we calculate \( x\% \) of \( y \):
\[ x\% \text{ of } y = \frac{x}{100} \times y = \frac{xy}{100} \]

### Step 3: Calculate \( y\% \) of \( x \)
Next, we calculate \( y\% \) of \( x \):
\[ y\% \text{ of } x = \frac{y}{100} \times x = \frac{yx}{100} \]

### Step 4: Add the Two Results
Now we add the two results from Step 2 and Step 3:
\[ x\% \text{ of } y + y\% \text{ of } x = \frac{xy}{100} + \frac{yx}{100} \]
Since \( \frac{xy}{100} \) and \( \frac{yx}{100} \) are the same, we can combine them:
\[ = \frac{xy}{100} + \frac{xy}{100} = \frac{2xy}{100} \]

### Step 5: Simplify the Expression
Now we simplify \( \frac{2xy}{100} \):
\[ = \frac{2}{100} \times xy = \frac{1}{50} \times xy \]

### Final Answer
Thus, the value of \( x\% \) of \( y + y\% \) of \( x \) is:
\[ \frac{1}{50}xy \]