Poonam walks 20 km towards north. She turns right and walks 12 km. She turns…

When a path consists of straight-line legs separated by turns, first resolve every leg into its North-South and East-West displacement, using the rule that a right turn rotates the direction of travel 90 degrees clockwise and a left turn rotates it 90 degrees anticlockwise. Adding these displacements leg by leg gives the net East-West and North-South offset between the start and the finish; the straight-line distance between the two points is then the hypotenuse of these two net offsets, found with the Pythagorean theorem, while the compass direction is read off from the sign of each offset.

1. Start at O, facing North, and walk 20 km North: net offset so far is 0 km East-West, 20 km North.

2. Turn right (North to East) and walk 12 km East: net offset becomes 12 km East, 20 km North.

3. Turn left (East to North) and walk 24 km North: net offset becomes 12 km East, 44 km North.

4. Turn right (North to East) and walk 36 km East: net offset becomes 48 km East, 44 km North.

5. Rotate 90 degrees clockwise (East to South) and walk 24 km South, reaching the finishing point F: net offset becomes 48 km East, 20 km North.

So F is 48 km East and 20 km North of O; equivalently, O is 48 km West and 20 km South of F — that is, O lies in the South-West direction from F.

Cross-check: 48, 20 and the resulting distance form a scaled 5-12-13 Pythagorean triple (4×12, 4×5, 4×13), since 482 + 202 = 2304 + 400 = 2704 = 522, confirming the distance instantly without repeating the long calculation.

Hence the starting point is 52 km from the finishing point, in the South-West direction.