From a point Lokesh starts walking towards the south and after walking 30 metres he turns to his right and walks 20 metres, then he turns right again and walks 30 metres and finally he turns to his left and walks 40 metres. In which direction is he with reference to the starting point?

Introduction / Context:
Lokesh walks along a path with several right angle turns. The question asks only for his final direction relative to the starting point, not the exact distance. After completing the path, we must understand whether his final position lies north, south, east or west of where he began. This is a classic direction sense problem that can be solved using simple coordinate reasoning.

Given Data / Assumptions:
- Lokesh starts from a point and walks 30 m south. - He then turns right from facing south and walks 20 m. - He then turns right again and walks 30 m. - Finally, he turns left and walks 40 m. - Directions are standard and each turn is 90 degrees.

Concept / Approach:
We place the starting point at (0, 0), treat south as negative y and west as negative x, and evaluate each movement. The key idea is to determine the net horizontal and vertical displacement at the end of the path. The sign of the horizontal displacement tells us if he is east or west of the start, and the sign of the vertical displacement tells us if he is north or south. In this path, the vertical movements cancel, leaving a purely westward displacement.

Step-by-Step Solution:
1. Start at (0, 0). 2. Walk 30 m south: position becomes (0, -30). 3. Facing south, a right turn points west; walk 20 m west to (-20, -30). 4. From facing west, another right turn points north; walk 30 m north to (-20, 0). 5. From facing north, a left turn points west; walk 40 m west to (-60, 0). 6. Final position is (-60, 0), which is 60 m west of the starting point with no north south displacement.

Verification / Alternative check:
Add vertical legs separately: 30 m south followed by 30 m north results in net 0 vertical movement, so Lokesh ends up on the same east west line as the start. Horizontally, he moves 20 m west and another 40 m west, for a total of 60 m west. A diagram illustrates a rectangle formed by the first three legs, and the final leg extends further west along the same horizontal line. This clearly shows that he is directly west of the origin.

Why Other Options Are Wrong:
- East would require positive x displacement, but Lokesh has only westward movement. - South would require a negative y displacement at the end, but vertical movement cancels out. - South East and North West are diagonals, but the final position is purely west, not shifted north or south.

Common Pitfalls:
Mistakes often come from misinterpreting right and left turns when facing different directions. Another issue is forgetting that 30 m north cancels 30 m south. Keeping a small table of cumulative x and y values or drawing the path as segments on a grid makes it much easier to arrive at the correct direction without confusion.

Final Answer:
Lokesh is to the west of the starting point.