If 200% of 40% of x is equal to 40% of y,then x is what fraction of y?

Options

A. 0.1
B. 0.2
C. 0.5
D. 0.8

Answer

To solve the problem, we need to find the fraction of \( y \) that \( x \) represents, given that \( 200\% \) of \( 40\% \) of \( x \) is equal to \( 40\% \) of \( y \).

### Step-by-Step Solution:

1. **Convert percentages to decimals**:
- \( 200\% \) can be expressed as \( \frac{200}{100} = 2 \).
- \( 40\% \) can be expressed as \( \frac{40}{100} = 0.4 \).

2. **Calculate \( 200\% \) of \( 40\% \) of \( x \)**:
\[ 200\% \text{ of } 40\% \text{ of } x = 2 \times 0.4 \times x = 0.8x \]

3. **Calculate \( 40\% \) of \( y \)**:
\[ 40\% \text{ of } y = 0.4y \]

4. **Set the two expressions equal to each other**:
\[ 0.8x = 0.4y \]

5. **Rearrange the equation to express \( x \) in terms of \( y \)**:
\[ \frac{x}{y} = \frac{0.4}{0.8} \]

6. **Simplify the fraction**:
\[ \frac{0.4}{0.8} = \frac{4}{8} = \frac{1}{2} \]

7. **Conclude the relationship**:
- Thus, \( x \) is \( \frac{1}{2} \) of \( y \) or \( 0.5 \) of \( y \).

### Final Answer:
- \( x \) is \( 0.5 \) of \( y \).