One day, Raviraj left home and cycled 20 Km southwards, turned right and…

Concept: In a direction-sense (path-tracking) problem, track the net displacement along two independent axes — North-South and East-West — instead of the total distance walked. A right turn rotates the direction of travel 90° clockwise (North → East → South → West → North) and a left turn rotates it 90° counter-clockwise; equal movements on the same axis in opposite directions cancel exactly, leaving only the uncancelled leg(s) on each axis to combine for the straight-line distance back to the start.

Application: Tracing Raviraj's path step by step:

1. Facing South from home (A), he cycles 20 km South to point B.

2. He turns right (South → West) and cycles 10 km West to point C.

3. He turns right again (West → North) and cycles 20 km North to point D. This North leg is equal and opposite to the earlier South leg, so it cancels it exactly — D lies on the same West-East line as home A.

4. He turns left (North → West) and cycles 20 km West to point E.

5. Since D and A lie on the same line, the two West legs (10 km to C, then 20 km to E) run in the same direction and add directly: 10 + 20 = 30 km is the straight-line distance from E back to A.

Cross-check: Plotting coordinates confirms it — taking home as (0, 0) with South and West as negative: B = (0, -20), C = (-10, -20), D = (-10, 0), E = (-30, 0). The straight-line distance from E to home is |0 - (-30)| = 30 km, matching the 30 Km option.