Direction Sense

The door faces East, so the back side faces West. Starting point is the back side. Let this be (0,0). 1. Walks straight from back side (West) 50 m: Position (-50, 0). 2. Turns right (facing North), walks 50 m: Position (-50, 0+50) = (-50, 50). 3. Turns left (facing West), walks 25 m: Position (-50-25, 50) = (-75, 50). The final position is (-75, 50). The x-coordinate is negative (West) and the y-coordinate is positive (North). Therefore, Madan is in the North-West direction from his starting point. This matches option (2).

Let the starting position be (0,0). Directions: N(y+), S(y-), E(x+), W(x-). 1. Walks 20 m North: Position (0, 20). 2. Turns right (facing East), walks 30 m: Position (0+30, 20) = (30, 20). 3. Turns right (facing South), walks 35 m: Position (30, 20-35) = (30,-15). 4. Turns left (facing East), walks 15 m: Position (30+15,-15) = (45,-15). 5. Turns left (facing North), walks 15 m: Position (45,-15+15) = (45, 0). The final position is (45, 0). Compared to the origin (0,0), this is 45 m along the positive x-axis, which is East. He is 45 m East from his original position. This matches option (4).

Shyam walks in a square-like path. By applying Pythagoras theorem, the total distance from his starting point is 15 meters.