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?

Correct Option (C)

: South

Let the initial direction of walking from the house be South. The sequence of movements can be analyzed as follows:

• Initially, the person walks 100 m South from the house.
• Turns left, which corresponds to East, and walks 100 m. At this point, the position is 100 m South and 100 m East of the house.
• Again turns left, which corresponds to North, and walks 300 m. The net North-South displacement becomes 300 m (North) - 100 m (South) = 200 m North. The East-West displacement remains 100 m East.
• Finally, turns right, which corresponds to East, and walks 100 m to reach the office. The final position of the office is 200 m North and (100 m + 100 m) = 200 m East of the house.

A position located 200 m North and 200 m East of a reference point is precisely in the North-East direction. This aligns with the given condition that the office is exactly in the North-East direction from the house. Therefore, the initial direction of walking from the house was South.

Incorrect Options:

If the person were to commence walking in any of the other specified directions (North-West, West, or South-West) and subsequently follow the given sequence of turns and distances, the final displacement of the office relative to the house would not result in a North-East orientation. Each of these alternative initial directions would lead to a different final position, which would not correspond to the stated North-East location of the office from the house.