x ls 5 times longer than y. The percentage by which y is less than x is :

Options

A. 0.5
B. 0.4
C. 0.8
D. 0.7

Answer

To solve the problem step by step, we need to find the percentage by which \( y \) is less than \( x \), given that \( x \) is 5 times longer than \( y \).

### Step 1: Define the relationship between \( x \) and \( y \)
Given that \( x \) is 5 times longer than \( y \), we can express this relationship mathematically:
\[ x = 5y \]

### Step 2: Calculate the difference between \( x \) and \( y \)
Next, we need to find the difference between \( x \) and \( y \):
\[ x - y = 5y - y = 4y \]

### Step 3: Calculate the percentage by which \( y \) is less than \( x \)
The formula to find the percentage by which \( y \) is less than \( x \) is given by:
\[ \text{Percentage} = \left( \frac{x - y}{x} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{4y}{5y} \right) \times 100 \]

### Step 4: Simplify the expression
Now, simplify the fraction:
\[ \frac{4y}{5y} = \frac{4}{5} \]
Thus, the percentage becomes:
\[ \text{Percentage} = \left( \frac{4}{5} \right) \times 100 = 80\% \]

### Conclusion
Therefore, the percentage by which \( y \) is less than \( x \) is:
\[ \boxed{80\%} \]