Shahid and Rohit start from the same point in opposite directions. After each 1 km, Shahid always turns left and Rohit always turns right. Which of the following statements is correct ?

The correct option is: They meet after each has travelled 3 km.

Let us trace the path of both Shahid and Rohit step-by-step from their starting point, which we can define as the origin (0, 0) on a 2D coordinate plane.

Assume they start by moving along the y-axis. Let Shahid go north (upwards) and Rohit go south (downwards).

Traced Path for Shahid (turns left after each 1 km):
1. Start: Shahid is at (0, 0) facing North.
2. After 1 km: Shahid travels 1 km North to reach (0, 1). He turns left (West).
3. After 2 km: Shahid travels 1 km West to reach (-1, 1). He turns left (South).
4. After 3 km: Shahid travels 1 km South to reach (-1, 0).

Traced Path for Rohit (turns right after each 1 km):
1. Start: Rohit is at (0, 0) facing South.
2. After 1 km: Rohit travels 1 km South to reach (0, -1). He turns right (West).
3. After 2 km: Rohit travels 1 km West to reach (-1, -1). He turns right (North).
4. After 3 km: Rohit travels 1 km North to reach (-1, 0).

After both have travelled exactly 3 km, both Shahid and Rohit arrive at the point (-1, 0). Therefore, they meet after each has travelled 3 km.