Q9. Direction: Study the information given below carefully and answer the…

2023

Q9. Direction: Study the information given below carefully and answer the question that follows. Shubhanshi starts from point P, walks 6 m north and reaches point Q. At point Q, she turns right and reaches point R after walking 4 m. After reaching point R, she turns right and walks 3 m to reach point S. Further, she walks to point T which is 8 m to the west of point S. She further goes 5 m south to point U, turns left and walks 8 m to reach point V. Shubhanshi goes 2 m North from her final position V. Now, she is how far and in which direction from her initial position P?

  1. A.

    4 m, North

  2. B.

    4 m, West

  3. C.

    5 m, West

  4. D.

    4 m, East

Show answer & explanation

Correct answer: D

In direction-and-distance problems, plot the movement on a coordinate grid with North and East as the positive y- and x-axes. A right turn rotates the walker's facing 90 degrees clockwise and a left turn 90 degrees counter-clockwise; each straight leg then adds a signed displacement to either the North-South running total or the East-West running total. The final distance and direction from the start is found by comparing the NET North-South total against the NET East-West total, not by reading off any single leg in isolation.

Applying this to Shubhanshi's path, taking P as the origin (0, 0), with North as +y and East as +x:

  1. Walks 6 m North to Q: position becomes (0, 6).

  2. At Q she turns right (facing changes from North to East) and walks 4 m to R: position becomes (4, 6).

  3. At R she turns right (facing changes from East to South) and walks 3 m to S: position becomes (4, 3).

  4. Walks 8 m West to T: position becomes (-4, 3).

  5. Walks 5 m South to U: position becomes (-4, -2).

  6. At U she turns left (facing changes from South to East) and walks 8 m to V: position becomes (4, -2).

  7. Finally walks 2 m North from V: position becomes (4, 0).

Cross-check: summing the North-South legs independently, +6 (N), -3 (S), -5 (S), +2 (N), gives a net of 0, so the final point lies on the same horizontal line as P. Summing the East-West legs, +4 (E), -8 (W), +8 (E), gives a net of +4, that is 4 m East. This matches the coordinate trace: the final position (4, 0) is exactly 4 m to the East of the initial position P (0, 0).

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