Malti bought a TV for Rs. 8,800 including GST at 10%. What is the original cost of the TV ?

Options

A. Rs. 8,800
B. Rs. 8,000
C. Rs. 7,920
D. Rs. 9,600

Answer

To find the original cost of the TV that Malti bought for Rs. 8,800 including GST at 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**: The total price of the TV includes the original cost (let's denote it as \( CP \)) and the GST. The GST is 10% of the original cost.

2. **Express the GST**: Since the GST is 10%, we can express it as:
\[ \text{GST} = 10\% \text{ of } CP = \frac{10}{100} \times CP = \frac{1}{10} \times CP \]

3. **Calculate Total Price**: The total price (including GST) can be expressed as:
\[ \text{Total Price} = CP + \text{GST} = CP + \frac{1}{10} \times CP = CP \left(1 + \frac{1}{10}\right) = CP \left(\frac{10}{10} + \frac{1}{10}\right) = CP \left(\frac{11}{10}\right) \]

4. **Set Up the Equation**: We know from the question that the total price is Rs. 8,800. Therefore, we can set up the equation:
\[ CP \left(\frac{11}{10}\right) = 8800 \]

5. **Solve for CP**: To find the original cost \( CP \), we can rearrange the equation:
\[ CP = 8800 \times \frac{10}{11} \]

6. **Calculate the Value**:
\[ CP = 8800 \times \frac{10}{11} = 8800 \times 0.909090909 = 8000 \]

7. **Conclusion**: The original cost of the TV is Rs. 8,000.

### Final Answer:
The original cost of the TV is Rs. 8,000.

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