Correct Option (B)
Let the starting point be the origin (0,0). Assume Shahid initially moves along the positive x-axis (East) and Rohit along the negative x-axis (West).
- Shahid's path:
- After 1 km: Position (1,0). Turns left (North).
- After 2 km: Position (1,1). Turns left (West).
- After 3 km: Position (0,1). Turns left (South).
- Rohit's path:
- After 1 km: Position (-1,0). Turns right (North).
- After 2 km: Position (-1,1). Turns right (East).
- After 3 km: Position (0,1). Turns right (South).
After each has travelled 3 km, both Shahid and Rohit are at the position (0,1). Therefore, they meet at this point.
Incorrect Options:
- Option A: After both have travelled 2 km, the distance between them is 4 km.
- After 2 km, Shahid is at (1,1) and Rohit is at (-1,1).
- The distance between them is calculated as √[(1 - (-1))² + (1 - 1)²] = √[(2)² + (0)²] = √4 = 2 km.
- Thus, the statement is incorrect.
- Option C: They meet for the first time after each has travelled 4 km.
- As established, they meet after each has travelled 3 km.
- After 4 km, Shahid is at (0,0) and Rohit is at (0,0). They meet again at the starting point, but this is not their first meeting.
- Thus, the statement is incorrect.
- Option D: They go on without ever meeting again.
- Their paths are cyclical. They meet at 3 km and again at 4 km.
- Given the repetitive nature of their movements (turning left/right after every 1 km), they will continue to meet at regular intervals.
- Thus, the statement is incorrect.
