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?
- (a) North-West
- (b) West
- (c) South ✓ UPSC's answer
- (d) South-West
Why the answer is (c)
• Headings: first walk in direction h; turn left; turn left again (now opposite to h); turn right (back to the first left-turn direction).
• Net displacement = 100 along h + 100 left of h − 300 along h + 100 left of h = 200 opposite to h + 200 to the left of h.
• Try h = South: 200 opposite to South is 200 m North; left of South (facing South) is East, so 200 m East. Net 200 N + 200 E — exactly North-East.
• So he first walked South — option (c).
Why the other options are wrong
- (a) North-West
- Starting North-West, the net displacement is 200 m South-East + 200 m South-West, i.e. due South, not North-East.
- (b) West
- Starting West, the net displacement is 200 m East + 200 m South, i.e. South-East, not North-East.
- (d) South-West
- Starting South-West, the net displacement is 200 m North-East + 200 m South-East, i.e. due East, not North-East.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.