If the ratio of the cost price and selling price of an article is 5 : 3, then what will be the loss percentage?

Options

A. 20
B. 40
C. 45
D. 50

Answer

To find the loss percentage when the ratio of the cost price (CP) to the selling price (SP) is given as 5:3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of CP to SP is given as 5:3. This means:
- Let the Cost Price (CP) = 5 units
- Let the Selling Price (SP) = 3 units

2. **Determine if there is a Loss**:
Since the Selling Price (SP) is less than the Cost Price (CP), there is a loss.

3. **Calculate the Loss**:
Loss can be calculated using the formula:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Substituting the values:
\[ \text{Loss} = 5 \text{ units} - 3 \text{ units} = 2 \text{ units} \]

4. **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:
\[ \text{Loss Percentage} = \left( \frac{2 \text{ units}}{5 \text{ units}} \right) \times 100 \]
Simplifying this gives:
\[ \text{Loss Percentage} = \left( \frac{2}{5} \right) \times 100 = 40\% \]

5. **Final Answer**:
The loss percentage is **40%**.