Town D is 13 km towards the East of Town A. A bus starts from Town A and…

Concept: Direction-sense problems like this one are solved by mapping each straight leg onto a coordinate plane: treat East-West motion as horizontal displacement and North-South motion as vertical displacement, and apply the turn rule that facing any direction and turning right rotates the heading 90 degrees clockwise (North to East, East to South, South to West, West to North). The distance and direction required to reach a destination is then just the net vector between the traveller's final position and that destination.

Application:

1. Place Town A at the origin (0, 0). Since Town D is 13 km East of Town A, Town D is at (13, 0).

2. The bus starts facing West and travels 8 km West, reaching (-8, 0).

3. Facing West and turning right changes the heading to North, so the bus travels 5 km North to reach Town B at (-8, 5).

4. Facing North and turning right changes the heading to East, so the bus travels 21 km East, reaching (-8 + 21, 5) = (13, 5).

5. Comparing (13, 5) with Town D at (13, 0): the East-West coordinate already matches Town D's, and only a vertical gap of 5 km remains, with the bus positioned North of Town D.

6. Closing a 5 km gap on the North side requires travelling 5 km South, so the bus must travel 5 km South to reach Town D.

Cross-check: This can be checked independently by summing the East-West legs on their own: 8 km West + 21 km East nets to 13 km East, exactly matching Town D's position, while the only North-South leg is the 5 km North move to Town B. So the single displacement left to cancel is 5 km North, confirming that travelling 5 km South reaches Town D.