Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ?
60 metres
He ends 60 metres from where he began — option 3.
Track the movement step by step. Take the starting point as the origin, with north upwards and east to the right. A left turn is anticlockwise, a right turn clockwise, and each turn is judged from the direction he is currently facing.
| Step | Facing | Distance | Position after the step |
|---|---|---|---|
| Start | — | — | (0, 0) |
| 1. Walks north | North | 20 m | (0, 20) |
| 2. Turns left | West | 40 m | (−40, 20) |
| 3. Turns left again | South | 20 m | (−40, 0) |
| 4. Turns right | West | 20 m | (−60, 0) |
Read off the answer. The final position is (−60, 0) and the start was (0, 0). The two are on the same horizontal line, so no square root is needed :
\(\text{Distance}=\sqrt{(-60-0)^{2}+(0-0)^{2}}=60\ \text{m}\)
Why the north-south movement cancels. He walked 20 m north in step 1 and 20 m south in step 3, so the two exactly undo each other and he finishes on the same east-west line as his starting point. All that survives is the westward travel, 40 m in step 2 and 20 m in step 4, giving 60 m due west of the start.
The turn that catches people out is the fourth. After step 3 he is facing south, and a right turn from south is west — not east. Turning the wrong way there gives a final position of (−20, 0) and the answer 20 metres, which is option 2. Sketching the path, or writing the facing direction at every step as in the table above, is what prevents it.
Hence, the answer is 60 metres.
Similar Questions
Raj travelled from a point X straight to Y at a distance of 80 metres. He turned right and walked 50 metres, then again turned right and walked 70 metres. Finally, he turned right and walked 50 metres. How far is he from the starting point ?
Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
