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

examrobotsa's picture

Submitted by examrobotsa on

Q: 148 (IAS/2000)
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 destination is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,13,10,1,7,13,2

keywords: 

{'shortest distance': [0, 1, 0, 1], 'distance': [0, 3, 3, 3], 'km eastwards': [0, 1, 0, 0], 'destination': [0, 2, 2, 3], 'km': [0, 0, 2, 1], 'person': [3, 1, 18, 13], 'thrice': [3, 1, 3, 1]}

Let`s analyze the given information step by step to find the shortest distance between the starting point (A) and the destination (D):

1. The person travels 3 km eastwards from point A to B.

2. The person then turns left and travels thrice the distance from B to reach point C. Since the distance from B to C is three times the distance from A to B (3 km x 3 = 9 km), the person travels 9 km from B to C.

3. Next, the person turns left again and travels five times the distance he covered between A and B. Since the distance from A to B is 3 km, the person travels 5 x 3 = 15 km from C to reach the destination point D.

To find the shortest distance between A and D, we can visualize a right-angled triangle with sides of length 9 km, 12 km, and the hypotenuse being the shortest distance.

Using the Pythagorean theorem, we can calculate the shortest distance as follows:

Shortest distance = ?(9^2 + 12^2) = ?(81 + 144) = ?225 = 15 km

Therefore, the shortest distance between the starting point A and the destination D is 15 km.