After walking for 5 kms, I turned right and covered a distance of 2 km, then…
2025
After walking for 5 kms, I turned right and covered a distance of 2 km, then turned left and covered a distance of 6 km. In the end, I was moving towards the North. In which direction did I start the journey?
- A.
North
- B.
East
- C.
West
- D.
South
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: Turning right rotates the direction you are facing by 90° clockwise, and turning left rotates it by 90° counter-clockwise. Two turns taken in opposite senses — one right turn followed by one left turn (or vice versa) — always cancel out and restore the original facing direction, whatever that direction was.
Application:
Let the direction of the first 5 km leg (the direction the journey started in) be D.
Turning right rotates the facing direction 90° clockwise, to D + 90°; the 2 km leg is walked facing this new direction.
Turning left from there rotates the facing direction 90° counter-clockwise, back to (D + 90°) − 90° = D — so the final 6 km leg faces the very same direction as the first leg.
The question states the final leg is directed due North, so D = North — the journey therefore started facing North.
Cross-check: Assume the journey started facing North: turn right from North → face East, walk the 2 km leg East; turn left from East → face North again, walk the final 6 km leg North. This matches the given information that the last leg was towards the North, confirming the result.
Answer: The journey started in the North direction.