Titan sells a wrist watch to a wholesaler making a. profit of `10%`. The wholesaler, in turn, sells it to the retailer making a profit of `10%`. A customer purchases it by paying .₹ 990. Thus, the profit of retailer is `2(3)/11%`. What is the cost incurred by the Titan to produce it?

Options

A. 768
B. 750
C. 800
D. 820

Answer

To find the cost incurred by Titan to produce the wristwatch, we can follow these steps:

### Step 1: Understand the Selling Price and Profit Percentage
The customer purchases the wristwatch for ₹990. This price includes the profit made by the retailer.

**Hint:** Identify the selling price and the profit percentages at each stage of the sale.

### Step 2: Calculate the Selling Price of the Retailer
Let the cost price of the retailer be \( CP_r \). The retailer sells the watch at a profit of 10%. Thus, the selling price (SP) can be expressed as:
\[ SP_r = CP_r + 0.10 \times CP_r = 1.10 \times CP_r \]
Since the customer pays ₹990, we have:
\[ 1.10 \times CP_r = 990 \]
To find \( CP_r \):
\[ CP_r = \frac{990}{1.10} = 900 \]

**Hint:** Use the formula for selling price based on cost price and profit percentage.

### Step 3: Calculate the Selling Price of the Wholesaler
Let the cost price of the wholesaler be \( CP_w \). The wholesaler also sells the watch at a profit of 10%. Thus, the selling price can be expressed as:
\[ SP_w = CP_w + 0.10 \times CP_w = 1.10 \times CP_w \]
From the previous step, we know that the selling price for the retailer is ₹900, so:
\[ 1.10 \times CP_w = 900 \]
To find \( CP_w \):
\[ CP_w = \frac{900}{1.10} = 818.18 \]

**Hint:** Again, apply the selling price formula to find the cost price of the wholesaler.

### Step 4: Calculate the Cost Price of Titan
Let the cost price for Titan be \( CP_t \). The selling price for Titan to the wholesaler is:
\[ SP_t = CP_t + 0.10 \times CP_t = 1.10 \times CP_t \]
From the previous step, we know that the selling price for the wholesaler is ₹818.18, so:
\[ 1.10 \times CP_t = 818.18 \]
To find \( CP_t \):
\[ CP_t = \frac{818.18}{1.10} = 743.89 \]

**Hint:** Use the same selling price formula to find the cost price for Titan.

### Final Answer
The cost incurred by Titan to produce the wristwatch is approximately ₹743.89.

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