X sells a TV to Y at the gain of 10% and again cells it to Z at a loss of 10%. If Z pays Rs 9900 to Y, then the cost price of the TV for X is-

Options

A. Rs 9,900
B. Rs 10,000
C. Rs 11,000
D. None of these

Answer

To find the cost price of the TV for X, we can follow these steps:

1. **Define the Cost Price for X**:
Let the cost price of the TV for X be denoted as CP.

2. **Calculate the Selling Price for Y**:
X sells the TV to Y at a gain of 10%.
The selling price (SP) for Y can be calculated as:
\[ SP_Y = CP + 10\% \text{ of } CP = CP + \frac{10}{100} \times CP = CP \times \left(1 + \frac{10}{100}\right) = CP \times \frac{11}{10} \]

3. **Calculate the Selling Price for Z**:
Y sells the TV to Z at a loss of 10%.
The selling price for Z can be calculated as:
\[ SP_Z = SP_Y - 10\% \text{ of } SP_Y = SP_Y - \frac{10}{100} \times SP_Y = SP_Y \times \left(1 - \frac{10}{100}\right) = SP_Y \times \frac{90}{100} = SP_Y \times \frac{9}{10} \]

4. **Substitute SP_Y into SP_Z**:
Now substituting the expression for SP_Y into the equation for SP_Z:
\[ SP_Z = \frac{9}{10} \times \left(\frac{11}{10} \times CP\right) = \frac{9 \times 11}{10 \times 10} \times CP = \frac{99}{100} \times CP \]

5. **Set SP_Z Equal to the Amount Paid by Z**:
According to the problem, Z pays Rs 9900 to Y, so we set:
\[ \frac{99}{100} \times CP = 9900 \]

6. **Solve for CP**:
To find CP, we can rearrange the equation:
\[ CP = 9900 \times \frac{100}{99} = 9900 \times \frac{100}{99} \]
\[ CP = 10000 \]

Thus, the cost price of the TV for X is Rs 10,000.