If x is 20% less than y, then `(y - x)/(y) = ? `

Options

A. `(4)/(5)`
B. `(1)/(5)`
C. `(3)/(5)`
D. `(2)/(5)`

Answer

To solve the problem, we need to express the relationship between \( x \) and \( y \) mathematically, and then calculate the expression \( \frac{y - x}{y} \).

### Step-by-Step Solution:

1. **Understanding the relationship**:
We know that \( x \) is 20% less than \( y \). This can be expressed mathematically as:
\[ x = y - 0.2y = 0.8y \]

2. **Substituting \( x \) in the expression**:
We need to find the value of \( \frac{y - x}{y} \). Substituting \( x = 0.8y \) into the expression gives:
\[ \frac{y - x}{y} = \frac{y - 0.8y}{y} \]

3. **Simplifying the expression**:
Now, simplify the numerator:
\[ y - 0.8y = 0.2y \]
Therefore, the expression becomes:
\[ \frac{0.2y}{y} \]

4. **Cancelling \( y \)**:
Since \( y \) is in both the numerator and the denominator, we can cancel it out (assuming \( y \neq 0 \)):
\[ \frac{0.2y}{y} = 0.2 \]

5. **Expressing as a fraction**:
The decimal \( 0.2 \) can be expressed as a fraction:
\[ 0.2 = \frac{2}{10} = \frac{1}{5} \]

### Final Answer:
Thus, the value of \( \frac{y - x}{y} \) is:
\[ \frac{1}{5} \]