A man sells a scooter to his friend at 10% loss. If the friend sells it for Rs. 54000 and gains 20%. Find the original cost price of the scooter.

Answer

To find the original cost price of the scooter, we can follow these steps:

### Step 1: Understand the Selling Price of the Friend
The friend sells the scooter for Rs. 54,000 and gains 20%. This means that Rs. 54,000 is 120% of the price at which the friend bought the scooter.

### Step 2: Calculate the Cost Price for the Friend
Let the cost price of the scooter for the friend be \( CP_f \). Since he sells it at a gain of 20%, we can express this as:
\[ CP_f \times \frac{120}{100} = 54000 \]
This simplifies to:
\[ CP_f \times 1.2 = 54000 \]
To find \( CP_f \), we can rearrange the equation:
\[ CP_f = \frac{54000}{1.2} \]

### Step 3: Perform the Calculation
Now, we calculate \( CP_f \):
\[ CP_f = \frac{54000}{1.2} = 45000 \]
So, the cost price for the friend is Rs. 45,000.

### Step 4: Calculate the Original Cost Price of the Scooter
The man sells the scooter to his friend at a 10% loss. This means that the selling price for the man is 90% of the original cost price \( CP_m \). We can express this as:
\[ CP_m \times \frac{90}{100} = CP_f \]
Substituting the value of \( CP_f \):
\[ CP_m \times 0.9 = 45000 \]
To find \( CP_m \), we rearrange the equation:
\[ CP_m = \frac{45000}{0.9} \]

### Step 5: Perform the Calculation
Now, we calculate \( CP_m \):
\[ CP_m = \frac{45000}{0.9} = 50000 \]
Thus, the original cost price of the scooter is Rs. 50,000.

### Final Answer
The original cost price of the scooter is Rs. 50,000.

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