Arun sells a car to his friend Amit at `10%` loss. If Amit sells the car for 54000 and gains `20%` then the original cost price of the car was

Options

A. Rs. 25000
B. Rs. 37500
C. Rs. 50000
D. Rs. 60000

Answer

To find the original cost price of the car that Arun sold to Amit, we can break the problem down into two parts: first, we will determine Amit's cost price based on his selling price and profit, and then we will find Arun's original cost price based on the loss he incurred.

### Step-by-Step Solution:

1. **Determine Amit's Cost Price:**
- Amit sells the car for ₹54,000 and makes a profit of 20%.
- Let Amit's cost price be \( CP_A \).
- Since he makes a 20% profit, we can express this as:
\[ Selling Price = Cost Price + Profit \]
\[ 54000 = CP_A + 0.20 \times CP_A \]
- This can be rewritten as:
\[ 54000 = 1.20 \times CP_A \]
- To find \( CP_A \), we divide both sides by 1.20:
\[ CP_A = \frac{54000}{1.20} \]
- Calculating this gives:
\[ CP_A = 45000 \]

2. **Determine Arun's Original Cost Price:**
- Arun sells the car to Amit at a loss of 10%.
- Let Arun's original cost price be \( CP_R \).
- Since he sells at a loss of 10%, we can express this as:
\[ Selling Price = Cost Price - Loss \]
\[ 45000 = CP_R - 0.10 \times CP_R \]
- This can be rewritten as:
\[ 45000 = 0.90 \times CP_R \]
- To find \( CP_R \), we divide both sides by 0.90:
\[ CP_R = \frac{45000}{0.90} \]
- Calculating this gives:
\[ CP_R = 50000 \]

### Conclusion:
The original cost price of the car was **₹50,000**.