If x is 6 times of y then y is less than x in percentage is

Options

A. `600%`
B. `83.3%`
C. `42.2%`
D. `60%`

Answer

To solve the problem, we need to find out how much less \( y \) is than \( x \) in percentage terms, given that \( x \) is 6 times \( y \).

### Step-by-Step Solution:

1. **Define the Relationship**:
- We know from the problem that \( x = 6y \).

2. **Find the Difference**:
- The difference between \( x \) and \( y \) can be calculated as:
\[ \text{Difference} = x - y = 6y - y = 5y \]

3. **Calculate the Percentage**:
- To find out how much less \( y \) is than \( x \) in percentage, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{x} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Percentage} = \left( \frac{5y}{6y} \right) \times 100 \]

4. **Simplify the Expression**:
- The \( y \) terms cancel out:
\[ \text{Percentage} = \left( \frac{5}{6} \right) \times 100 \]
- Now, calculate \( \frac{5}{6} \):
\[ \frac{5}{6} \approx 0.8333 \]
- Therefore:
\[ \text{Percentage} = 0.8333 \times 100 \approx 83.33\% \]

5. **Final Answer**:
- Thus, \( y \) is approximately \( 83.33\% \) less than \( x \).