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 ?
10 metres
He ends 10 metres from where he started — option 4.
Set it out step by step. Take X as the origin and let the first leg run north; each right turn is a quarter turn clockwise.
| Leg | Facing | Distance | Position |
|---|---|---|---|
| Start at X | — | — | (0, 0) |
| 1. X to Y | North | 80 m | (0, 80) |
| 2. Turns right | East | 50 m | (50, 80) |
| 3. Turns right | South | 70 m | (50, 10) |
| 4. Turns right | West | 50 m | (0, 10) |
Read off the answer. He finishes at (0, 10) and started at (0, 0) :
\(\text{Distance}=\sqrt{(0-0)^{2}+(10-0)^{2}}=10\ \text{m}\)
The quick way. Four right turns in succession trace a rectangle, so the east-west legs must cancel and the north-south legs partly cancel :
| Direction | Out | Back | Net |
|---|---|---|---|
| North-south | 80 m north | 70 m south | 10 m north |
| East-west | 50 m east | 50 m west | 0 |
Since the sideways movement cancels exactly, the answer is simply the difference of the two lengthwise legs, 80 − 70 = 10 metres, and no square root is needed at all.
Where candidates go wrong. Some subtract the wrong pair — 50 from 80, giving 30, which is option 1 — and some apply Pythagoras to 30 and 50 out of habit. The safeguard is to notice before calculating that the two 50-metre legs are in opposite directions and therefore cancel; the figure is three sides of a rectangle plus a return, not an L-shape.
Hence, the answer is 10 metres.
Similar Questions
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 ?
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?
