Question

A person starts from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D the shortest distance between the starting point and the destination is :

• A. 18KM
• B. 12KM
• C. 16KM
• D. 15KM

Answer 1

Answer:

D. 15KM

The shortest distance between the starting point and the destination is 15 km.

• Point A to B (East): The person walks 3 km East.

  • Position of B: 3 km East from A.

• Point B to C (North): Turning left means heading North. The distance is thrice AB ($3 \times 3\text{ km} = \mathbf{9\text{ km}}$).

  • Position of C: 3 km East, 9 km North.

• Point C to D (West): Turning left again means heading West. The distance is five times AB ($5 \times 3\text{ km} = \mathbf{15\text{ km}}$).

  • Position of D: Since they move 15 km West from a point that was 3 km East, they end up 12 km West of the starting line, and 9 km North.

Calculating the Shortest Distance (A to D)

This forms a right-angled triangle where:

• Base (Horizontal distance): 12 km

• Height (Vertical distance): 9 km

Using the Pythagorean theorem ($a^2 + b^2 = c^2$):
$\text{Distance} = \sqrt{12^2 + 9^2}$
$\text{Distance} = \sqrt{144 + 81}$
$\text{Distance} = \sqrt{225} = \mathbf{15\text{ km}}$