An article is sold at 5% profit instead of 8% loss, the man gains Rs 260 more. What is the cost price (in Rs) of the article?

Options

A. 1800
B. 2000
C. 1500
D. 1400

Answer

To solve the problem step by step, let's denote the cost price of the article as \( CP \).

1. **Understanding the Selling Prices**:
- When the article is sold at an 8% loss, the selling price (SP) can be calculated as:
\[ SP_1 = CP - (8\% \text{ of } CP) = CP - 0.08 \times CP = 0.92 \times CP \]
- When the article is sold at a 5% profit, the selling price is:
\[ SP_2 = CP + (5\% \text{ of } CP) = CP + 0.05 \times CP = 1.05 \times CP \]

2. **Finding the Difference in Selling Prices**:
- According to the problem, the difference between the selling prices when sold at 5% profit and 8% loss is Rs 260:
\[ SP_2 - SP_1 = 260 \]
- Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ (1.05 \times CP) - (0.92 \times CP) = 260 \]

3. **Simplifying the Equation**:
- Combine like terms:
\[ 1.05CP - 0.92CP = 260 \]
\[ 0.13CP = 260 \]

4. **Solving for Cost Price (CP)**:
- To find \( CP \), divide both sides by 0.13:
\[ CP = \frac{260}{0.13} \]
\[ CP = 2000 \]

Thus, the cost price of the article is Rs 2000.