Explanation:

- Muneesh sold the motorcycle for Rs. 38720 at a 10% profit.

- Let the cost price for Muneesh be \( x \).

- \( 1.1x = 38720 \).

- Solving for \( x \), we find \( x = 35200 \).

- Rajiv sold to Muneesh at a 20% loss.

- Let the cost price for Rajiv be \( y \).

- \( 0.8y = 35200 \).

- Solving for \( y \), we find \( y = 44000 \).

- Lalit sold to Rajiv at a 10% profit.

- Let the initial cost price (including repairs) for Lalit be \( z \).

- \( 1.1z = 44000 \).

- Solving for \( z \), we find \( z = 40000 \).

- Lalit spent Rs. 500 on repairs. Therefore, the initial price paid by Lalit is \( 40000 - 500 = 39500 \).

The correct answer is Option 4: Rs. 39500