The cost price of an article is 25% less than its selling price. What is the profit or loss percentage?

Options

A. 33.33%, loss
B. 66.67%, profit
C. 33.33%, profit
D. 66.67%, loss

Answer

To solve the problem step by step, we need to determine the profit or loss percentage based on the given information that the cost price (CP) of an article is 25% less than its selling price (SP).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
- Let the Selling Price (SP) be represented as \( SP \).
- According to the problem, the Cost Price (CP) is 25% less than the Selling Price. This can be expressed mathematically as:
\[ CP = SP - 0.25 \times SP = 0.75 \times SP \]

2. **Calculating Profit**:
- Profit is calculated as the difference between Selling Price and Cost Price:
\[ \text{Profit} = SP - CP \]
- Substituting the expression for CP:
\[ \text{Profit} = SP - (0.75 \times SP) = 0.25 \times SP \]

3. **Calculating Profit Percentage**:
- The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
- We already found that Profit is \( 0.25 \times SP \) and \( CP = 0.75 \times SP \). Now substituting these values into the profit percentage formula:
\[ \text{Profit Percentage} = \left( \frac{0.25 \times SP}{0.75 \times SP} \right) \times 100 \]

4. **Simplifying the Expression**:
- The \( SP \) in the numerator and denominator cancels out:
\[ \text{Profit Percentage} = \left( \frac{0.25}{0.75} \right) \times 100 \]
- Simplifying \( \frac{0.25}{0.75} \) gives:
\[ \frac{0.25}{0.75} = \frac{1}{3} \]
- Therefore:
\[ \text{Profit Percentage} = \frac{1}{3} \times 100 = 33.33\% \]

5. **Conclusion**:
- The profit percentage is \( 33.33\% \).

### Final Answer:
The profit percentage is **33.33%**.