A wholesaler sells a watch to a retailer at a profit of 8% and the retailer sells it to a customer at a profft of 12%. If the customer pays Rs. 8,448 what had it cost (approximately) tothe wholesaler (in Rs)?

Options

A. 6984
B. 6082
C. 7120
D. 7022

Answer

To find the cost price of the watch to the wholesaler, we can follow these steps:

### Step 1: Understand the Selling Price (SP) and Profit Percentages
The customer pays Rs. 8,448 for the watch. The retailer sells it at a profit of 12%. This means the selling price (SP) of the retailer can be expressed in terms of the cost price (CP) of the retailer.

### Step 2: Calculate the Retailer's Cost Price (CP)
Let the cost price of the retailer be \( CP_r \). Since the retailer sells at a profit of 12%, we can write the equation for the selling price (SP) as:
\[ SP_r = CP_r + (12\% \text{ of } CP_r) = CP_r \times (1 + \frac{12}{100}) = CP_r \times 1.12 \]
Given that \( SP_r = 8,448 \), we can set up the equation:
\[ CP_r \times 1.12 = 8,448 \]

### Step 3: Solve for the Retailer's Cost Price (CP)
To find \( CP_r \), we rearrange the equation:
\[ CP_r = \frac{8,448}{1.12} \]
Calculating this gives:
\[ CP_r = \frac{8,448}{1.12} = 7,557.14 \text{ (approximately)} \]

### Step 4: Calculate the Wholesaler's Cost Price (CP)
Now, we need to find the cost price of the watch to the wholesaler. The wholesaler sells the watch to the retailer at a profit of 8%. Let the cost price of the wholesaler be \( CP_w \). The selling price (SP) from the wholesaler to the retailer can be expressed as:
\[ SP_w = CP_w + (8\% \text{ of } CP_w) = CP_w \times (1 + \frac{8}{100}) = CP_w \times 1.08 \]
Since \( SP_w = CP_r \), we can write:
\[ CP_r = CP_w \times 1.08 \]
Substituting \( CP_r \) from our previous calculation:
\[ 7,557.14 = CP_w \times 1.08 \]

### Step 5: Solve for the Wholesaler's Cost Price (CP)
Rearranging gives:
\[ CP_w = \frac{7,557.14}{1.08} \]
Calculating this gives:
\[ CP_w = \frac{7,557.14}{1.08} = 6,986.00 \text{ (approximately)} \]

### Final Answer
The cost to the wholesaler is approximately Rs. 6,986.

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