Raman sells a machine for Rs. 39 lakh at a loss. Had he sold it for Rs. 49 lakh, his gain would have been three times the loss. What is the cost price of the machine?

Options

A. Rs. 46.5 lakh.
B. Rs. 62 lakh
C. Rs. 36.5 lakh
D. Rs. 41.5 lakh

Answer

To solve the problem, we need to determine the cost price of the machine based on the information provided about the selling price and the loss incurred.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost price (CP) of the machine be Rs. x lakh.

2. **Calculate Loss:**
Since Raman sells the machine for Rs. 39 lakh at a loss, we can express the loss as:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = x - 39 \]

3. **Calculate Gain if Sold at Rs. 49 lakh:**
If Raman had sold the machine for Rs. 49 lakh, the gain would be:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = 49 - x \]

4. **Set Up the Equation:**
According to the problem, the gain from selling at Rs. 49 lakh is three times the loss incurred from selling at Rs. 39 lakh. Therefore, we can set up the equation:
\[ 49 - x = 3(x - 39) \]

5. **Expand and Simplify the Equation:**
Expanding the right side:
\[ 49 - x = 3x - 117 \]
Now, rearranging the equation:
\[ 49 + 117 = 3x + x \]
\[ 166 = 4x \]

6. **Solve for x:**
Dividing both sides by 4:
\[ x = \frac{166}{4} = 41.5 \]

7. **Conclusion:**
The cost price of the machine is Rs. 41.5 lakh.

### Final Answer:
The cost price of the machine is Rs. 41.5 lakh.

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