The selling price of an article is `(5)/(6)` times the cost price, What is the loss percentage (correct up to two decimal places)?

Options

A. `16.67%`
B. `15.48%`
C. `13.67%`
D. `12.50%`

Answer

To solve the problem, we need to find the loss percentage when the selling price (SP) of an article is \(\frac{5}{6}\) times the cost price (CP).

### Step-by-Step Solution:

1. **Define Variables**:
Let the cost price (CP) be \( x \).

2. **Calculate Selling Price**:
According to the problem, the selling price (SP) is given by:
\[ SP = \frac{5}{6} \times CP = \frac{5}{6} \times x \]

3. **Determine Loss**:
The loss incurred can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the values we have:
\[ \text{Loss} = x - \frac{5}{6}x \]
To simplify, we can factor out \( x \):
\[ \text{Loss} = x \left(1 - \frac{5}{6}\right) = x \left(\frac{1}{6}\right) = \frac{x}{6} \]

4. **Calculate Loss Percentage**:
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left(\frac{\frac{x}{6}}{x}\right) \times 100 \]
Simplifying this gives:
\[ \text{Loss Percentage} = \left(\frac{1}{6}\right) \times 100 = \frac{100}{6} \approx 16.67 \]

5. **Final Result**:
Therefore, the loss percentage is approximately \( 16.67\% \).