A man sells a car to his friend at 10% loss. If the friend sells it for 54.000 and gains 20%, the original cost price of the car was

Options

A. Rs 25,000
B. Rs 35,000
C. Rs 45,000
D. Rs 50,000

Answer

To find the original cost price of the car, we can break down the problem into a few steps:

### Step 1: Determine the Cost Price for the Friend
The friend sells the car for ₹54,000 and gains 20%. We can use the formula for selling price (SP) related to cost price (CP) and gain percentage (GP):

\[ SP = CP \times \left(1 + \frac{GP}{100}\right) \]

Rearranging this formula to find the cost price for the friend (CP_friend):

\[ CP_{friend} = \frac{SP}{1 + \frac{GP}{100}} \]

Substituting the values:

\[ CP_{friend} = \frac{54000}{1 + \frac{20}{100}} = \frac{54000}{1.2} = 45000 \]

### Step 2: Determine the Selling Price for the Man
The cost price for the friend (₹45,000) is actually the selling price for the man (SP_man) who sold the car at a 10% loss.

### Step 3: Calculate the Original Cost Price for the Man
We know that the selling price can also be calculated using the loss percentage:

\[ SP = CP \times \left(1 - \frac{Loss}{100}\right) \]

Rearranging this to find the cost price for the man (CP_man):

\[ CP_{man} = \frac{SP_{man}}{1 - \frac{Loss}{100}} \]

Substituting the values:

\[ CP_{man} = \frac{45000}{1 - \frac{10}{100}} = \frac{45000}{0.9} = 50000 \]

### Conclusion
Thus, the original cost price of the car was ₹50,000.

### Final Answer
The original cost price of the car is **₹50,000** (Option D).

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