Town D is 13 km to the East of Town A. A bus starts from Town A, travels 8 km…

In direction-and-distance problems, fix the starting point at coordinates (0, 0) and track East–West movement on one axis and North–South movement on the other; each turn only changes the axis of the next leg. The answer to 'how far and which way to reach a target point' is simply the gap between the traveller's current position and the target, found by comparing the two coordinates.

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

2. The bus travels 8 km West from A, reaching (−8, 0).

3. Facing West, a right turn changes the heading to North. Travelling 5 km North brings the bus to Town B at (−8, 5).

4. Facing North, the next right turn changes the heading to East. Travelling 21 km East moves the x-coordinate from −8 to −8 + 21 = 13, giving the bus's stopping point as (13, 5).

5. Comparing (13, 5) with Town D at (13, 0): the x-coordinates already match, so only the y-coordinate differs — by 5 units.

6. Since the bus's y-coordinate (5) is greater than Town D's (0), the bus is North of Town D, so it must travel 5 km South to reach it.

Cross-check using only the East–West totals: the bus travels 8 km West then 21 km East, a net 21 − 8 = 13 km East of A — exactly Town D's East offset — confirming the bus and Town D share the same East–West position. The only outstanding gap is the 5 km North–South offset built up on the single North leg, closed by heading South.