A man gets Rs 13 more by selling an article at a profit of 12 `1/2` % and than selling it at a loss of 12 `1/2`%. The cost price of the article is:

Options

A. 25.5
B. 38
C. 52
D. 65

Answer

To solve the problem, we need to find the cost price (CP) of an article based on the information given about selling it at a profit and a loss.

### Step-by-Step Solution:

1. **Understanding the Profit and Loss Percentages**:
- The man sells the article at a profit of 12.5% and at a loss of 12.5%.
- Profit of 12.5% means he sells it for 112.5% of the cost price.
- Loss of 12.5% means he sells it for 87.5% of the cost price.

2. **Setting Up the Equations**:
- Let the cost price of the article be \( CP \).
- Selling price at a profit of 12.5%:
\[ SP_{profit} = CP + 0.125 \times CP = 1.125 \times CP \]
- Selling price at a loss of 12.5%:
\[ SP_{loss} = CP - 0.125 \times CP = 0.875 \times CP \]

3. **Finding the Difference in Selling Prices**:
- According to the problem, the difference between the selling price at profit and the selling price at loss is Rs 13:
\[ SP_{profit} - SP_{loss} = 13 \]
- Substituting the selling prices:
\[ 1.125 \times CP - 0.875 \times CP = 13 \]

4. **Simplifying the Equation**:
- Combine the terms:
\[ (1.125 - 0.875) \times CP = 13 \]
\[ 0.25 \times CP = 13 \]

5. **Calculating the Cost Price**:
- To find \( CP \), divide both sides by 0.25:
\[ CP = \frac{13}{0.25} = 52 \]

6. **Conclusion**:
- The cost price of the article is Rs 52.

### Final Answer:
The cost price of the article is Rs 52.