Question Details

Anil starts from point A and drives 8 km towards North. He then takes a right turn, drives 2 km, turns right and drives 11 km. He then takes a right turn and drives 5 km. He takes a final right turn, drives 3 km and stops at point P. How far (shortest distance) and towards which direction should he drive in order to reach point A again? (All turns are 90 degrees turns only unless specified.)

Options

A

3 km towards East

B

2 km towards East

C

2 km towards West

D

3 km towards North

Show Answer

Correct Answer :

Option A

3 km towards East

Solution :

The correct option is 3 km towards East.

To find the shortest distance and direction from the final position P to the starting point A, we can map the entire journey on a two-dimensional coordinate system. Let us set the starting point A at the origin (0,0) where:
- North corresponds to the positive y-axis.
- South corresponds to the negative y-axis.
- East corresponds to the positive x-axis.
- West corresponds to the negative x-axis.

Let's trace Anil's path step-by-step:
1. Start at Point A: (0,0).
2. Drive 8 km North: Moving along the positive y-axis brings Anil to:
(0,8).
3. Turn right and drive 2 km: A right turn from North is East (positive x-direction). Moving 2 km East brings him to:
(2,8).
4. Turn right and drive 11 km: A right turn from East is South (negative y-direction). Moving 11 km South brings him to:
(2,8-11)=(2,-3).
5. Turn right and drive 5 km: A right turn from South is West (negative x-direction). Moving 5 km West brings him to:
(2-5,-3)=(-3,-3).
6. Turn right and drive 3 km to stop at P: A right turn from West is North (positive y-direction). Moving 3 km North brings him to his final point P:
(-3,-3+3)=(-3,0).

Now, we find the relative position of the starting point A (0,0) from point P (-3,0):
- The difference in x-coordinates is 0-(-3)=3 km (towards the positive x-direction, which is East).
- The difference in y-coordinates is 0-0=0 km.

Thus, point P is located 3 km West of point A. In order to return to point A from point P, Anil must travel a shortest distance of 3 km towards East.

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