If 40 percent of x is equal to 160 percent of y, what is the value of `(x)/(y)`?

Options

A. `(1)/(12)`
B. `(1)/(4)`
C. `4`
D. `20`

Answer

To solve the problem, we need to find the value of \( \frac{x}{y} \) given that 40 percent of \( x \) is equal to 160 percent of \( y \).

### Step-by-Step Solution:

1. **Convert percentages to fractions**:
We start with the equation given in the problem:
\[ 40\% \text{ of } x = 160\% \text{ of } y \]
This can be expressed mathematically as:
\[ \frac{40}{100} \cdot x = \frac{160}{100} \cdot y \]

2. **Simplify the fractions**:
We can simplify both fractions:
\[ \frac{40}{100} = \frac{2}{5} \quad \text{and} \quad \frac{160}{100} = \frac{8}{5} \]
So, we rewrite the equation as:
\[ \frac{2}{5} x = \frac{8}{5} y \]

3. **Eliminate the fractions**:
To eliminate the fractions, we can multiply both sides by 5:
\[ 2x = 8y \]

4. **Rearrange the equation**:
Now, we can rearrange this equation to express \( \frac{x}{y} \):
\[ \frac{x}{y} = \frac{8}{2} \]

5. **Simplify the ratio**:
Simplifying \( \frac{8}{2} \) gives us:
\[ \frac{x}{y} = 4 \]

### Final Answer:
Thus, the value of \( \frac{x}{y} \) is \( 4 \).