Rahul moves 5 km towards the South from his initial position and then takes a left turn to move 5 km.\nAgain, he takes another left turn and moves 10 km, and finally he moves 5 km towards the West.\nIn which direction is he now located from his initial position?

Introduction / Context:
This direction sense question describes Rahul walking along several straight segments involving two left turns and one final absolute movement towards the West. We are asked to determine only the final direction of Rahul with respect to his starting point, not the exact distance. By breaking his route into horizontal and vertical displacements, we can identify whether he ends up North, South, East, West or in one of the diagonal quadrants relative to the initial position.

Given Data / Assumptions:

• Rahul starts from an initial position.
• He moves 5 km towards the South.
• He then takes a left turn and moves 5 km.
• Again, he takes a left turn and moves 10 km.
• Finally, he moves 5 km towards the West (absolute direction).
• All turns are 90 degree turns.
• We assume that from facing South, a left turn leads to East, and from facing East, a left turn leads to North.

Concept / Approach:
We model Rahul's path on a coordinate grid, converting each movement into x (East–West) and y (North–South) components. By adding up all the components, we get his final coordinates relative to the origin. The sign and magnitude of the final coordinates tell us the direction in which he lies from the starting point. In this case, we will find that the net horizontal displacement is zero, while there is a net positive vertical displacement, indicating a final direction of North.

Step-by-Step Solution:
Step 1: Place Rahul's initial position at (0, 0). Step 2: Moving 5 km South takes him to (0, -5); he is facing South. Step 3: From facing South, a left turn makes him face East. Moving 5 km East takes him to (5, -5). Step 4: From facing East, another left turn makes him face North. Moving 10 km North takes him to (5, 5). Step 5: Finally, he moves 5 km towards the West, which is an absolute direction. This changes only the x-coordinate, moving him from (5, 5) to (0, 5). Step 6: The final coordinates are (0, 5). Compared with the starting point (0, 0), Rahul is 5 km North and 0 km East–West. Hence he is directly North of his starting point.

Verification / Alternative check:
We can verify by separately summing the vertical and horizontal components. For vertical movement, he goes 5 km South and then 10 km North, giving a net displacement of 10 − 5 = 5 km North. For horizontal movement, he goes 5 km East and 5 km West, which cancel out to zero. With a positive net North component and zero East–West component, his final direction must be exactly North of the starting position. A rough sketch of the path confirms that he ends up above the starting point in a straight vertical line.

Why Other Options Are Wrong:
West would require a net horizontal displacement to the left of the origin, but we found that East and West movements cancel entirely. East is similarly ruled out because there is no net rightward movement. South is incorrect because Rahul ends up North of the starting point, not below it. South-West would require both Southward and Westward net displacement; neither condition holds once cancellations are considered.

Common Pitfalls:
Many candidates treat the final Westward movement as if it dominates the path, forgetting that earlier Eastward movement cancels it. Others misinterpret left turns from South and East, sometimes swapping East and West or North and South. Keeping a simple coordinate tally or drawing the path step by step is the best way to avoid these errors and quickly see the true final direction.

Final Answer:
Rahul is finally located directly to the North of his initial position.