Saroj starts walking towards South and walks 10 km. He then turns left and…

In direction-and-distance problems, movement is tracked along two perpendicular axes: North-South and East-West. Two walks of equal length in exactly opposite directions cancel each other out completely, so only the net movement along each axis matters. When the final net movement lies entirely along a single axis, the straight-line distance from the starting point equals the sum of the movements along that axis; when it lies along both axes, the distance is found using the Pythagorean rule: distance = square root of (x squared + y squared).

1. Saroj starts at the origin O and walks 10 km South.

2. He turns left. Facing South, a left turn points him East. He walks 5 km East.

3. He turns left again. Facing East, a left turn points him North. He walks 10 km North -- this exactly cancels the 10 km walked South in Step 1, since both are the same length on the North-South axis.

4. He turns right. Facing North, a right turn points him East. He walks 20 km East, adding to the East-West distance already covered.

5. Net North-South displacement = 0 km (fully cancelled). Net East-West displacement = 5 km + 20 km = 25 km, all in the same (East) direction.

6. Since the entire net displacement lies along one axis (East), the straight-line distance from the starting point is simply 25 km.

Cross-check using coordinates: place the origin at (0, 0) with East as the positive x-axis and North as the positive y-axis. South 10 km leads to (0, -10); East 5 km leads to (5, -10); North 10 km leads to (5, 0); East 20 km leads to (25, 0). The distance from (0, 0) to (25, 0) is 25 km, confirming the result.