Find the loss percentage when the cost price and selling price of an article are in the ratio of 5 : 3.

Options

A. `40%`
B. `35%`
C. `45%`
D. `26%`

Answer

To find the loss percentage when the cost price (CP) and selling price (SP) of an article are in the ratio of 5:3, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Ratios**:
Let the cost price (CP) be represented as \( 5X \) and the selling price (SP) as \( 3X \), where \( X \) is a common multiplier.

2. **Calculate the Loss**:
Loss is calculated as:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Substituting the values, we get:
\[ \text{Loss} = 5X - 3X = 2X \]

3. **Calculate the Loss Percentage**:
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Loss Percentage} = \left( \frac{2X}{5X} \right) \times 100 \]

4. **Simplify the Expression**:
The \( X \) cancels out:
\[ \text{Loss Percentage} = \left( \frac{2}{5} \right) \times 100 \]
Now calculating:
\[ \text{Loss Percentage} = 40\% \]

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

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