If the cost price of 3 items is equal to selling price of 5 items. How much loss in percentage will be made ?

Options

A. `20%`
B. `30%`
C. `40%`
D. `50%`

Answer

To solve the problem, we need to determine the loss percentage based on the given relationship between the cost price (CP) and selling price (SP) of the items.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
The problem states that the cost price of 3 items is equal to the selling price of 5 items.

Let the cost price of one item be \( CP \).

2. **Expressing Cost Price and Selling Price**:
- The cost price of 3 items is \( 3 \times CP \).
- Let the selling price of one item be \( SP \). Therefore, the selling price of 5 items is \( 5 \times SP \).

According to the problem, we have:
\[ 3 \times CP = 5 \times SP \]

3. **Finding the Selling Price in Terms of Cost Price**:
Rearranging the equation to find \( SP \):
\[ SP = \frac{3 \times CP}{5} \]

4. **Calculating the Loss**:
The loss incurred on selling one item can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the expression for \( SP \):
\[ \text{Loss} = CP - \frac{3 \times CP}{5} \]
To simplify:
\[ \text{Loss} = CP - 0.6 \times CP = 0.4 \times CP \]

5. **Calculating the Loss Percentage**:
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]
Substituting the loss value:
\[ \text{Loss Percentage} = \left( \frac{0.4 \times CP}{CP} \right) \times 100 = 0.4 \times 100 = 40\% \]

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