Sanmitra walks 8 metres towards the north. He then turns to his right and walks 16 metres, turns to his left and walks 5 metres, and again turns to his left and walks 16 metres. In which direction is he now from his starting point?

Difficulty: Easy

Correct Answer: North

Explanation:


Introduction / Context:
This direction sense problem describes a walk with several turns forming a rectangular path. We are asked to determine the final direction of Sanmitra from his starting point. Rather than requiring the exact distance, the question focuses only on the relative orientation, which can often be answered by carefully comparing total north south and east west movements.


Given Data / Assumptions:

  • Sanmitra walks 8 m north.
  • He turns right from facing north and walks 16 m east.
  • He turns left from facing east and walks 5 m north.
  • He turns left again from facing north and walks 16 m west.
  • We need the direction of his final position relative to the starting point.


Concept / Approach:
Use coordinates for clarity. Take the starting point as (0, 0). North increases y, south decreases y, east increases x, and west decreases x. After each movement we update the coordinates and then see in which quadrant the final point lies. If the final x is zero and y is positive, he is directly north of the starting point, and so on.


Step-by-Step Solution:
Start at (0, 0). Walk 8 m north to reach (0, 8). Facing north, a right turn leads east; walk 16 m east to reach (16, 8). Facing east, a left turn leads north; walk 5 m north to reach (16, 13). Facing north, a left turn leads west; walk 16 m west to reach (0, 13). Final coordinates are (0, 13), meaning he is directly north of his starting point.


Verification / Alternative check:
Horizontally, Sanmitra moves 16 m east and then 16 m west, which cancel out. Vertically, he moves 8 m north and then another 5 m north, with no southward movement, giving a total of 13 m north. Therefore, his final position is directly north of where he started, without any east west offset.


Why Other Options Are Wrong:
Option A: South would require a net movement downward, which does not occur here.
Option B: East would require a remaining positive x coordinate, but the net x is zero.
Option D: West would require a negative x coordinate, which is also not the case.
Option E: None of these is incorrect because North is explicitly listed and correct.


Common Pitfalls:
One common mistake is assuming that returning 16 m west immediately brings him back to the starting point, ignoring the additional 5 m north that was covered. Another error is misidentifying right and left turns when not initially facing north. A clear x y coordinate tracking eliminates such confusion.


Final Answer:
Sanmitra is finally in the North direction from his starting point.

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