X and Y start from the same point. X walks 40 m towards the north, then turns towards the west and walks 80 m, and then turns to his right and walks 50 m. At the same time, Y walks 90 m towards the north in a straight line. Where is Y now with respect to the position of X?

Introduction / Context:
This problem combines direction sense with relative positioning of two people who start together but follow different routes. Such questions are highly relevant for exams because they test a candidate's ability to simultaneously track more than one path and then compare their final positions diagrammatically or numerically. Learning a systematic approach reduces the chance of confusion when several turns and distances are involved.

Given Data / Assumptions:

• X and Y both start from the same initial point.
• X walks 40 m towards the north.
• Then X turns towards the west and walks 80 m.
• Next X turns to his right and walks 50 m.
• During this time, Y walks straight 90 m towards the north from the starting point.
• All paths are straight and turns are right angles.

Concept / Approach:
We set up a coordinate system with the starting point as (0, 0). We then track the movement of each person separately. For X we account for the three legs with turns. For Y we account for a single straight path towards the north. Once we have final coordinates for both, the relative position of Y with respect to X is simply the vector difference between these coordinates, which translates into a descriptive answer like 80 m east of X.

Step-by-Step Solution:
Step 1: Start both X and Y at the origin (0, 0).Step 2: For X, move 40 m north to reach (0, 40).Step 3: From there X turns west and moves 80 m, giving position (-80, 40).Step 4: X is now facing west. A right turn from west means facing north. Moving 50 m north changes the y coordinate to 90, so X reaches (-80, 90).Step 5: For Y, from the origin (0, 0), moving 90 m north directly leads to the position (0, 90).Step 6: Now we compare X at (-80, 90) and Y at (0, 90). Both have the same y coordinate 90, so they are on the same east west line. The x coordinates differ by 80 units, with Y at 0 and X at -80. Therefore, Y is 80 m to the east of X.

Verification / Alternative check:
We can visualise the situation by noting that X and Y end up at the same north south level, both having travelled a total of 90 m north in different stages. However, X also travels 80 m west that is never counterbalanced by any eastward movement. Y does not move west or east at all. So relative to X, Y must be 80 m east. This geometric reasoning matches the coordinate computation and confirms the answer.

Why Other Options Are Wrong:
Options A and C that mention 30 m east or west are incorrect because they are based on a mistaken difference in north south displacement rather than horizontal distance. Option B (80 m west) reverses the direction, placing Y incorrectly to the west of X. Only option D correctly states that Y is 80 m east of X, capturing both magnitude and direction properly.

Common Pitfalls:
Students sometimes compare each leg of movement individually rather than the final positions, which can lead to mixing up distances. Another pitfall is misinterpreting the right turn from west, which must give north, not south. Keeping a small sketch and marking the intermediate points reduces such errors. Always compute or sketch the final coordinates and then compare rather than making a judgment midway.

Final Answer:
Y is located 80 m to the east of X, so the correct option is “Y is 80 m to the East of X”.