An article is sold at 10% profit instead of 5% loss, the man gains Rs 75 more. What is the cost price (in Rs) of that article?

Options

A. 250
B. 200
C. 500
D. 225

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understanding the Problem**:
- We need to find the cost price (CP) of an article.
- The article is sold at a 10% profit instead of a 5% loss, resulting in an additional gain of Rs 75.

2. **Assuming the Cost Price**:
- Let's assume the cost price (CP) of the article is Rs 100. (This is a common technique to simplify calculations.)

3. **Calculating Selling Prices**:
- If the article is sold at a 5% loss, the selling price (SP) would be:
\[ SP_{loss} = CP - (5\% \text{ of } CP) = 100 - 5 = Rs 95 \]
- If the article is sold at a 10% profit, the selling price would be:
\[ SP_{profit} = CP + (10\% \text{ of } CP) = 100 + 10 = Rs 110 \]

4. **Finding the Difference in Selling Prices**:
- The difference between the selling prices when sold at a 10% profit and a 5% loss is:
\[ SP_{profit} - SP_{loss} = 110 - 95 = Rs 15 \]

5. **Relating the Difference to the Extra Gain**:
- According to the problem, this difference of Rs 15 corresponds to the additional gain of Rs 75.
- Therefore, we can set up the ratio:
\[ 15\% \text{ of CP} = Rs 75 \]

6. **Calculating the Cost Price**:
- To find the cost price, we can set up the equation:
\[ \frac{15}{100} \times CP = 75 \]
- Rearranging gives:
\[ CP = \frac{75 \times 100}{15} \]
- Simplifying this:
\[ CP = \frac{7500}{15} = 500 \]

7. **Conclusion**:
- The cost price of the article is Rs 500.