Titan sells a wrist watch to a wholsaler making a profit of 10%. The wholeseler, in turn, sells it to the retailer making a profit of 10%. A customer purchases it by paying Rs. 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 will follow these steps:

### Step 1: Understand the Selling Price and Profit
Titan sells the wristwatch to the wholesaler at a profit of 10%. This means that if the cost price for Titan is \( C_T \), the selling price \( S_W \) to the wholesaler can be expressed as:
\[ S_W = C_T + 0.10 \times C_T = 1.10 \times C_T \]

### Step 2: Wholesaler's Selling Price
The wholesaler then sells the wristwatch to the retailer, also at a profit of 10%. Therefore, the selling price \( S_R \) to the retailer can be expressed as:
\[ S_R = S_W + 0.10 \times S_W = 1.10 \times S_W \]
Substituting \( S_W \) from Step 1:
\[ S_R = 1.10 \times (1.10 \times C_T) = 1.10^2 \times C_T = 1.21 \times C_T \]

### Step 3: Retailer's Selling Price
The customer purchases the wristwatch for Rs. 990. Thus, we have:
\[ S_R = 990 \]
From Step 2, we can set up the equation:
\[ 1.21 \times C_T = 990 \]

### Step 4: Solve for Titan's Cost Price
Now, we can solve for \( C_T \):
\[ C_T = \frac{990}{1.21} \]

Calculating this gives:
\[ C_T = 990 \div 1.21 \approx 818.18 \]

### Step 5: Final Calculation
To find the exact value, we can use the fraction:
\[ C_T = \frac{990 \times 100}{121} = \frac{99000}{121} \approx 818.18 \]

### Conclusion
The cost incurred by Titan to produce the wristwatch is approximately Rs. 818.18.

---