A wholesaler sells a jacket to retailer at a profit of 5% and the retailer 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 out the cost price to the wholesaler, we can follow these steps:

### Step 1: Determine the cost price for the retailer
The customer pays Rs. 4158 for the jacket, which includes a profit of 10% for the retailer. We can use the formula for selling price (SP) to find the cost price (CP) for the retailer:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

Given that the profit percentage is 10%, we can express this as:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Substituting the known values:

\[ 4158 = \text{CP}_{\text{retailer}} \times \left(1 + \frac{10}{100}\right) \]

This simplifies to:

\[ 4158 = \text{CP}_{\text{retailer}} \times 1.10 \]

### Step 2: Calculate the cost price for the retailer
Now, we can solve for \(\text{CP}_{\text{retailer}}\):

\[ \text{CP}_{\text{retailer}} = \frac{4158}{1.10} \]

Calculating this gives:

\[ \text{CP}_{\text{retailer}} = \frac{4158}{1.10} = 3780 \text{ Rs.} \]

### Step 3: Determine the cost price for the wholesaler
Next, we need to find the cost price for the wholesaler. The retailer bought the jacket at a profit of 5%. We can use the same formula:

\[ \text{CP}_{\text{retailer}} = \text{CP}_{\text{wholesaler}} \times \left(1 + \frac{5}{100}\right) \]

Substituting the known values:

\[ 3780 = \text{CP}_{\text{wholesaler}} \times 1.05 \]

### Step 4: Calculate the cost price for the wholesaler
Now, we can solve for \(\text{CP}_{\text{wholesaler}}\):

\[ \text{CP}_{\text{wholesaler}} = \frac{3780}{1.05} \]

Calculating this gives:

\[ \text{CP}_{\text{wholesaler}} = \frac{3780}{1.05} = 3600 \text{ Rs.} \]

### Final Answer
Thus, the cost price to the wholesaler is Rs. 3600.

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