Direction Test: Ravi left home and cycled 10 km towards South, then turned…

Concept: In a direction-sense problem, track displacement along two perpendicular axes (north-south and east-west). Every 90° turn (left or right) rotates the current heading by a quarter turn; movements in exactly opposite directions along the same axis cancel each other, and the final straight-line distance back to the start is the resultant of the net displacement along each axis (by the Pythagorean theorem when both axes have a nonzero net).

Application:

1. Start at home and face South. Cycle 10 km South — the position is now 10 km South of home.

2. Turn right (from South, a right turn faces West). Cycle 5 km West.

3. Turn right again (from West, a right turn faces North). Cycle 10 km North — this exactly cancels the earlier 10 km South leg, so the net north-south displacement returns to zero.

4. Turn left (from North, a left turn faces West). Cycle 10 km West — combined with the earlier 5 km West leg, the net east-west displacement is 5 + 10 = 15 km West of home.

Cross-check: Since the net north-south displacement is 0 km and the net east-west displacement is 15 km, the straight-line distance back home is √(0² + 15²) = 15 km — confirming the result without needing to retrace the path.

Result: He must cycle 15 km in a straight line to reach home.