If the ratio of selling price and cost price is 3:4 respectively, then what is the loss percentage ?

Options

A. `10%`
B. `33.33%`
C. `20%`
D. `25%`

Answer

To find the loss percentage when the ratio of selling price (SP) to cost price (CP) is given as 3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of selling price to cost price is given as 3:4. This means:
\[ \frac{SP}{CP} = \frac{3}{4} \]

2. **Assign Variables**:
Let the selling price (SP) be \(3x\) and the cost price (CP) be \(4x\), where \(x\) is a common multiplier.

3. **Calculate Loss**:
Loss is calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the values we assigned:
\[ \text{Loss} = 4x - 3x = x \]

4. **Calculate Loss Percentage**:
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{x}{4x}\right) \times 100 = \left(\frac{1}{4}\right) \times 100 \]
Simplifying this gives:
\[ \text{Loss Percentage} = 25\% \]

### Final Answer:
The loss percentage is **25%**.