Arjun is facing east. He first walks 10 metres in the east direction. Then he turns left and walks another 10 metres. Next, he turns right and walks 25 metres. From there he walks 10 metres towards the south. Finally, he walks 50 metres towards his left. How far, in metres, is he now from his original starting position?

Introduction / Context:
This direction sense question combines several orthogonal movements (east, north, south) with left and right turns. We are required to find the straight line distance between Arjun's starting point and his final position, after he traverses a somewhat rectangular path and then makes a long final move. These problems test a candidate's ability to track position step by step and then use basic geometry to find the net displacement.

Given Data / Assumptions:

• Arjun initially faces east.
• He walks 10 metres east.
• He then turns left (towards north) and walks 10 metres.
• Next he turns right (towards east) and walks 25 metres.
• From there he walks 10 metres towards the south.
• Finally he walks 50 metres towards his left, relative to his last facing direction.
• All turns are right angle turns.
• We must calculate the straight line distance from his original position to his final position.

Concept / Approach:
We will model the situation on a coordinate plane. Treat Arjun's starting point as (0, 0). East is positive x, west negative x, north positive y, south negative y. Each movement changes either x or y while the other coordinate remains constant. After tracking all five legs of the journey, we compute the net horizontal and vertical displacement, then apply Pythagoras: distance = square root of (x^2 + y^2).

Step-by-Step Solution:
Step 1: Start at (0, 0), facing east. After walking 10 metres east, Arjun is at (10, 0). Step 2: From facing east, a left turn makes him face north. Walking 10 metres north, he reaches (10, 10). Step 3: From facing north, a right turn takes him back to facing east. Walking 25 metres east, he moves to (35, 10). Step 4: He then walks 10 metres south, so his y coordinate decreases by 10, giving a new position (35, 0). Step 5: At this point he is facing south (because his last movement was south). From facing south, his left side is east. Walking 50 metres towards his left means 50 metres east, so he moves to (85, 0). Step 6: The final coordinates are (85, 0). This means he is 85 metres east of the starting point with no north-south displacement. Step 7: The straight line distance from (0, 0) to (85, 0) is simply 85 metres.

Verification / Alternative check:
We can compute net horizontal and vertical components directly. Horizontally, Arjun moves 10 metres east in the first leg, 25 metres east in the third leg, and 50 metres east in the final leg, for a total of 10 + 25 + 50 = 85 metres east. There is no westward motion. Vertically, he moves 10 metres north and then 10 metres south, which cancel each other out, leaving zero net vertical displacement. Hence the displacement vector is purely horizontal with magnitude 85 metres, confirming our coordinate reasoning.

Why Other Options Are Wrong:

• Option B, 80 metres, may come from forgetting one of the eastward segments.
• Option C, 75 metres, could arise from incorrectly adding 10, 25 and 40 instead of 50 for the last leg.
• Option D, 90 metres, results from naive addition of an extra 5 metres somewhere without justification.
• Option E, 70 metres, is a random underestimation not supported by the exact calculations.

Common Pitfalls:
Students often misinterpret which direction is left when the person is facing south or west. Another common issue is mixing up total distance walked with net displacement. Total distance is the sum of all segments, but displacement considers only the straight line between start and finish. Drawing a quick sketch with arrows corresponding to each step usually clarifies the path and prevents these errors.

Final Answer:
Arjun is now 85 metres away from his starting point, directly to the east, so the required distance is 85 metres.