A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?

1. A. North-West
2. B. West
3. C. South
4. D. South-West

Answer: C

Explanation

Let’s assume the person initially walks North and trace the path:
1. Starts at (0,0), walks 100m North: (0, 100).
2. Turns left (now facing West), walks 100m: (-100, 100).
3. Turns left (now facing South), walks 300m: (-100, 100 – 300) = (-100, -200).
4. Turns right (now facing West), walks 100m: (-100 – 100, -200) = (-200, -200).
In this hypothetical scenario, the office is at (-200, -200) relative to the house (0,0), which is in the South-West direction.

The problem states that the office is actually in the North-East direction. South-West is exactly opposite to North-East (180 degrees apart).
This means our initial assumption for the starting direction was 180 degrees off. If assuming North led to South-West, then the actual starting direction must be 180 degrees opposite to North, which is South.

Let’s verify with an initial South direction:
1. Starts at (0,0), walks 100m South: (0, -100).
2. Turns left (now facing East), walks 100m: (100, -100).
3. Turns left (now facing North), walks 300m: (100, -100 + 300) = (100, 200).
4. Turns right (now facing East), walks 100m: (100 + 100, 200) = (200, 200).
The office is at (200, 200) relative to the house (0,0), which is indeed in the North-East direction. Thus, he initially walked South. This question tests direction sense and spatial reasoning.