Two jackets were bought at the same cost. One was sold at a profit of `9%` and the other at a profit of `15%`. If the difference in the selling price of both the jackets was Rs. 105, then what was the cost price of each jacket ?

Options

A. Rs. 1155
B. Rs. 1750
C. Rs. 1050
D. Rs. 950

Answer

To solve the problem, let's denote the cost price of each jacket as \( CP \).

1. **Calculate the Selling Price of Each Jacket:**
- For the first jacket sold at a profit of 9%, the selling price (SP1) can be calculated as:
\[ SP1 = CP + (9\% \text{ of } CP) = CP + 0.09 \times CP = 1.09 \times CP \]
- For the second jacket sold at a profit of 15%, the selling price (SP2) can be calculated as:
\[ SP2 = CP + (15\% \text{ of } CP) = CP + 0.15 \times CP = 1.15 \times CP \]

2. **Set Up the Equation for the Difference in Selling Prices:**
- According to the problem, the difference in selling prices of the two jackets is Rs. 105. Therefore, we can write:
\[ SP2 - SP1 = 105 \]
- Substituting the expressions for SP1 and SP2:
\[ (1.15 \times CP) - (1.09 \times CP) = 105 \]

3. **Simplify the Equation:**
- Combine like terms:
\[ (1.15 - 1.09) \times CP = 105 \]
\[ 0.06 \times CP = 105 \]

4. **Solve for the Cost Price (CP):**
- To find \( CP \), divide both sides of the equation by 0.06:
\[ CP = \frac{105}{0.06} \]
- Calculate \( CP \):
\[ CP = 1750 \]

5. **Conclusion:**
- The cost price of each jacket is Rs. 1750.