From his house, Atul travels 10 kms to the east. Then he turned left and…
2023
From his house, Atul travels 10 kms to the east. Then he turned left and covered 5 kms and then he turned right and covered 6 kms. He turned again to his left and covered 5 kms. He then turned to his left and covered 20 kms. Finally, he turned to his right and covered 5 kms. In which direction is he from his starting point ?
Answer: D. North-West — Concept: In a direction-and-distance problem, a Left turn rotates the walker's facing 90° counter-clockwise and a Right turn rotates it 90° clockwise — always…
- A.
North-East
- B.
South-East
- C.
South-West
- D.
North-West
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Show answer & explanation
Correct answer: D
Concept:
In a direction-and-distance problem, a Left turn rotates the walker's facing 90° counter-clockwise and a Right turn rotates it 90° clockwise — always relative to the CURRENT facing, not the original heading. Track the facing after every turn, then add each leg's distance along the east–west (x) and north–south (y) axes to get the net displacement; the sign of the final (x, y) pair fixes the compass quadrant: (+x, +y) = North-East, (+x, −y) = South-East, (−x, −y) = South-West, (−x, +y) = North-West.
Application:
Start facing East at (0, 0). Move 10 km east, reaching (10, 0). Facing: East.
Left turn changes facing from East to North. Move 5 km north, reaching (10, 5). Facing: North.
Right turn changes facing from North to East. Move 6 km east, reaching (16, 5). Facing: East.
Left turn changes facing from East to North. Move 5 km north, reaching (16, 10). Facing: North.
Left turn changes facing from North to West. Move 20 km west, reaching (-4, 10). Facing: West.
Right turn changes facing from West to North. Move 5 km north, reaching (-4, 15). Facing: North.
Cross-check:
Grouping the legs by axis independently confirms this: eastward legs total 10 + 6 = 16 km and the only westward leg is 20 km, giving a net x of 16 − 20 = −4 (4 km west); northward legs total 5 + 5 + 5 = 15 km with no southward leg, giving a net y of +15 (15 km north). Since x is negative and y is positive, the final point lies in the (−x, +y) quadrant, which is North-West of the starting point.
Therefore, Atul is North-West of his starting point.