Saroj walks 24 km towards north. She turns right and walks 20 km. She turns…

Concept

In a direction-sense problem, fix a coordinate grid with North as +y and East as +x, then update the position after each move while tracking the current facing. "Turn right/left" rotates the facing 90 degrees relative to the way you are heading; "rotate clockwise" turns the facing 90 degrees clockwise on the compass (N to E to S to W). The net displacement between two points comes from Pythagoras, and the compass direction comes from the signs of the East and North offsets.

Tracing each move (start facing North at the origin)

1. Walk 24 km North -> position (0, 24); still facing North.

2. Turn right -> now facing East; walk 20 km -> (20, 24).

3. Turn left -> now facing North; walk 30 km -> (20, 54).

4. Rotate 90 degrees clockwise (North to East); walk 15 km -> (35, 54).

5. Turn right -> now facing South; walk 30 km -> (35, 24).

6. Rotate 90 degrees clockwise (South to West); walk 25 km -> (10, 24).

Finishing point versus starting point

The finishing point is at (10, 24): 10 km East and 24 km North of the start. The question asks for the starting point measured from the finishing point, so reverse the offsets: the start lies 10 km West and 24 km South of the finish, i.e. to the South-west.

Distance = sqrt(102 + 242) = sqrt(100 + 576) = sqrt(676) = 26 km.

Cross-check

This is a 10-24-26 triangle (exactly twice the 5-12-13 Pythagorean triple), confirming the 26 km distance. Both offsets point from the finish back toward the start to the West and South, so the bearing of the starting point from the finishing point is South-west, matching 26 km, South-west.