From his house, Lokesh went 15 km to the North. Then he turned west and…
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From his house, Lokesh went 15 km to the North. Then he turned west and covered 10 km. Then he turned south and covered 5 km. Finally turning to the east, he covered 10 km. In which direction is he from his house?
- A.
North
- B.
South
- C.
East
- D.
West
Show answer & explanation
Correct answer: A
Concept: In direction-and-distance problems, resolve the path into two independent axes — the north–south axis and the east–west axis. Equal-and-opposite movements along an axis cancel out completely, and the final position relative to the start is fixed only by the net displacement left on each axis.
Application: Track the position leg by leg.
Take the house as the starting point (0, 0).
Walking 15 km North moves him to (0, 15).
Turning west and walking 10 km moves him to (−10, 15).
Turning south and walking 5 km moves him to (−10, 10).
Turning east and walking 10 km moves him to (0, 10).
Cross-check: Checking axis by axis gives the same result: the two horizontal legs (10 km west and 10 km east) are equal in length, so they cancel and leave zero net east–west shift; the two vertical legs leave a net of 15 km − 5 km = 10 km northward. Both checks agree that the final point (0, 10) lies 10 km due north of the house, so Lokesh is to the North of his house.
