Facing the east, Rahul first turns towards his left and walks 10 metres. Then he again turns towards his left and walks another 10 metres. After that he turns towards his right and walks straight for 25 metres. In which direction is Rahul now standing with respect to his original starting point?

Introduction / Context:
Direction sense questions often involve a person starting in a known direction, then making several left and right turns, and finally asking about the direction of the final position relative to the starting point. In this problem Rahul starts facing east and makes a sequence of moves. We must track both his positions and facing directions carefully to conclude the final direction of his location from the starting point.

Given Data / Assumptions:

• Rahul initially faces east at his starting point.
• He turns left and walks 10 metres.
• He then turns left again and walks another 10 metres.
• After that, he turns right and walks straight for 25 metres.
• All turns are right angles.
• We need the direction of Rahul's final position relative to the starting point, not the direction he is facing.

Concept / Approach:
A reliable technique is to place the starting point at the origin of a coordinate plane. We represent east as the positive x direction, west as negative x, north as positive y, and south as negative y. As Rahul turns left or right, his facing direction changes accordingly, and each movement updates his coordinates. After the sequence of movements, we compare his final coordinates with the origin to determine the direction: if x is positive and y is positive, the point lies in the north east quadrant, if x is negative and y is positive it lies in the north west, and so on.

Step-by-Step Solution:
Step 1: Suppose Rahul starts at point O with coordinates (0, 0), facing east. Step 2: From facing east, a left turn means he now faces north. Walking 10 metres north moves him to (0, 10). Step 3: From facing north, another left turn makes him face west. Walking 10 metres west moves him to (-10, 10). Step 4: From facing west, a right turn makes him face north again. He now walks 25 metres north, so his final position becomes (-10, 35). Step 5: His final coordinates are (-10, 35). The x coordinate is negative and the y coordinate is positive. Step 6: A point with negative x and positive y lies in the north west quadrant, so Rahul is to the north west of his starting point.

Verification / Alternative check:
We may visualise the path without coordinates. Starting from the origin facing east, the first left turn sends Rahul north for 10 metres. The second left turn sends him west for 10 metres, placing him diagonally north west of the origin. The final right turn sends him north again for an additional 25 metres, which means he moves even further north while remaining west of the starting point. Therefore he must be somewhere north west of the starting point, which confirms the coordinate calculation.

Why Other Options Are Wrong:

• Option B, North-East, would require Rahul to be east of the origin, which conflicts with his 10 metre movement west in the middle of the path.
• Option C, South-West, would require a negative y coordinate; however he keeps moving north overall, ending with a large positive y value.
• Option D, South-East, also contradicts the overall movement, as he never ends up south of the starting point and does move west.
• Option E, West, would be correct only if his final vertical position aligned with the starting point, which is not the case because he is 35 metres north.

Common Pitfalls:
Many students confuse the direction of left and right turns when the facing direction is not the usual north. For example, from west a right turn leads to north, not south. Another common error is to focus on the last movement and forget earlier shifts that move the person west or north. Sketching the path or using a coordinate grid is an excellent way to avoid such mistakes and gives a clear visual representation of the final location.

Final Answer:
Rahul's final position is to the North-West of his starting point.