Rahul walks 30 metres towards the south. Then he turns to his right and walks straight for another 30 metres. Next he turns to his left and walks 20 metres, and then turns to his left again and walks 30 metres. After completing this route, how far is he from his initial position?

Introduction / Context:
This direction and distance problem describes Rahul moving along four line segments with right and left turns. The task is to determine his straight line distance from his starting position after finishing the entire path. This requires translating the path into horizontal and vertical components and then using the distance formula to compute the net displacement.

Given Data / Assumptions:

• Rahul walks 30 m south from his initial position.
• He then turns right from facing south and walks 30 m west.
• He then turns left from facing west and walks 20 m south.
• He finally turns left from facing south and walks 30 m east.
• Distances are in metres and all turns are right angles.

Concept / Approach:
We use a coordinate plane. Let the starting point be (0, 0). South decreases the y coordinate, north increases it, east increases x, and west decreases x. Once we determine the final coordinates, the straight line distance from the origin is obtained using the formula distance = sqrt(x^2 + y^2). Observing cancellations between opposite directions can also simplify reasoning.

Step-by-Step Solution:
Start at (0, 0). Walk 30 m south to reach (0, -30). Facing south, a right turn leads west; walk 30 m west to reach (-30, -30). Facing west, a left turn leads south; walk 20 m south to reach (-30, -50). Facing south, a left turn leads east; walk 30 m east to reach (0, -50). Final coordinates are (0, -50), meaning Rahul is 50 m south of his starting point. Straight line distance from start = sqrt(0^2 + 50^2) = 50 m.

Verification / Alternative check:
Horizontally, Rahul moves 30 m west and 30 m east, which cancel out completely. Vertically, he first moves 30 m south, then an additional 20 m south, for a total of 50 m south. With no horizontal displacement remaining, his straight line distance from the start is exactly his southward displacement, 50 m.

Why Other Options Are Wrong:
Option B: 30 m only accounts for part of the southward movement.
Option C: 10 m is far too small and ignores the overall path.
Option D: 60 m exceeds the total southward movement and is not supported by the net displacement.
Option E: None of these is incorrect because 50 metres is explicitly listed and correctly matches the analysis.

Common Pitfalls:
Students sometimes add all segment lengths to estimate displacement or confuse intermediate positions with the final location. Another pitfall is misinterpreting left turns from non north orientations. A small grid sketch or a table of x y values for each step is an efficient defence against these mistakes.

Final Answer:
Rahul is 50 metres away from his initial position.