The ratio of selling price to the cost price is 13 : 17. What is the loss percentage?

Options

A. 23.52
B. 27.74
C. 18.62
D. 19.45

Answer

To solve the problem of finding the loss percentage when the ratio of selling price (SP) to cost price (CP) is given as 13:17, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the selling price (SP) be represented as \( 13x \) and the cost price (CP) be represented as \( 17x \), where \( x \) is a common multiplier.

2. **Calculate the Loss**:
The loss can be calculated using the formula:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Substituting the values we have:
\[ \text{Loss} = 17x - 13x = 4x \]

3. **Calculate the Loss Percentage**:
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{4x}{17x} \right) \times 100 \]

4. **Simplify the Expression**:
The \( x \) terms cancel out:
\[ \text{Loss Percentage} = \left( \frac{4}{17} \right) \times 100 \]

5. **Calculate the Final Value**:
Now, calculate \( \frac{4}{17} \times 100 \):
\[ \text{Loss Percentage} = \frac{400}{17} \approx 23.52\% \]

### Final Answer:
The loss percentage is approximately **23.52%**.

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