A man starts from his house and walks 10 km in South direction, then he turns…

2024

A man starts from his house and walks 10 km in South direction, then he turns right and goes 6 km, again he turns right and goes 10 km and finally turns right and goes 6 km. At what distance is he from the starting point and in which direction?

  1. A.

    2 km, North

  2. B.

    3 km, South

  3. C.

    At the starting point

  4. D.

    4 km, East

Show answer & explanation

Correct answer: C

Concept: In direction-test problems, track a fixed compass frame rather than a rotating 'forward' frame. Starting while facing South, each 'turn right' rotates the current heading 90 degrees clockwise, in the cycle South, West, North, East, South. Represent every leg walked as a vector and find the net displacement by summing the North-South components together and the East-West components together separately.

Application:

  1. Leg 1: facing South, walks 10 km South, reaching a position 10 km South of the start.

  2. Turn right changes the heading from South to West. Leg 2: walks 6 km West, reaching 10 km South and 6 km West of the start.

  3. Turn right changes the heading from West to North. Leg 3: walks 10 km North, cancelling the earlier southward distance and returning to the same latitude as the start, 6 km West of the start.

  4. Turn right changes the heading from North to East. Leg 4: walks 6 km East, cancelling the earlier westward distance and returning to the exact starting point.

Cross-check: The two North-South legs are 10 km South and 10 km North, which sum to zero net vertical displacement; the two East-West legs are 6 km West and 6 km East, which sum to zero net horizontal displacement. Both components cancel exactly.

Result: He ends up exactly at the starting point, at zero distance from it.

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