Ravi started walking towards East. After moving a distance of 1 km, he turned Southwards and walked 5 km. Again he turned to east and walked 2 km. Finally he turned to the North and walked 9 km. How far is he from his starting point?

Set the starting point as the origin, with East as positive x and North as positive y. Track each leg. East 1 km takes Ravi to (1, 0). South 5 km takes him to (1, -5). East 2 km takes him to (3, -5). North 9 km takes him to (3, 4). His displacement from the start is therefore the straight line from (0, 0) to (3, 4).

By Pythagoras, the distance is sqrt(3² + 4²) = sqrt(25) = 5 km, which is option B.

• A (7 km): Wrong. This is not a sum of the legs. Distance walked is 17 km, but displacement is what matters here.
• C (4 km): Wrong. This is only the net north-south change (9 - 5 = 4). It ignores the 3 km eastward displacement.
• D (3 km): Wrong. This is only the net east-west change (1 + 2 = 3). It ignores the 4 km northward displacement.

Core concept: displacement is a vector. Resolve the motion into perpendicular components, add them separately, then combine using Pythagoras. This is the standard direction-sense and distance method in the reasoning section of the Prelims paper, and the same habit helps with map-based questions.

Trap: Aspirants either add all the distances or stop after finding only one net component. Always find both the net east-west and net north-south movement before combining them.