A wholesaler sells a jacket to a retaller at a profit of 5% and the retaller sells it to a customer at a profit of 10%. If the customer pays Rs. 4158, what had it cost (in Rs.) to the wholesaler?

Options

A. 3500
B. 3400
C. 3300
D. 3600

Answer

To find the cost price of the jacket for the wholesaler, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Selling Prices**:
- The wholesaler sells the jacket to the retailer at a profit of 5%.
- The retailer sells the jacket to the customer at a profit of 10%.

2. **Let the Cost Price of the Wholesaler be \( x \)**:
- The selling price (SP) of the wholesaler to the retailer can be calculated as:
\[ SP_{\text{wholesaler}} = x + 0.05x = 1.05x \]

3. **Calculate the Selling Price of the Retailer**:
- The retailer sells the jacket at a profit of 10% on the price he bought it for (which is the SP of the wholesaler):
\[ SP_{\text{retailer}} = SP_{\text{wholesaler}} + 0.10 \times SP_{\text{wholesaler}} = 1.10 \times SP_{\text{wholesaler}} = 1.10 \times 1.05x = 1.155x \]

4. **Set Up the Equation**:
- According to the problem, the customer pays Rs. 4158 for the jacket. Therefore, we can set up the equation:
\[ 1.155x = 4158 \]

5. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 1.155:
\[ x = \frac{4158}{1.155} \]

6. **Calculate \( x \)**:
- Performing the division:
\[ x \approx 3600 \]

7. **Conclusion**:
- The cost price of the jacket for the wholesaler is Rs. 3600.

### Final Answer:
The cost to the wholesaler is Rs. 3600.

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