M4maths Previous Puzzles

11 Jul 2012 shortest distance

A man travels 300 m north then 200 m east then 300sqrt(2) m south-west. Shortest distance between initial and final point will be

OPtion

1) 50 m
2) 100sqrt(2) m
3) 50sqrt(2) m
4) 100 m
5) 200 m
6) 500+300sqrt(2) m
7) 100+300sqrt(2) m
8) 400 m
9) 20 m
10) none of these

Solution

300sqrt(2) along west-south means 300 m along west and 300 m along south.
300 m along north is recovered by 300 m along south, and 200 m east and 300 m west means 100 m along west.
you can understand it by taking a diagram.
[shortest distance means direct distance (displacement) between initial and final point.]

Correct Option: 4 Best Solution (2)

jyotish r   12 years AGO

here we have to find the one side of a right triangle with hypotenuse (300-200)(2^.5)=100(2^.5) and another side (300-200)=100.clearly it is 100 by pythagoras theorem.

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Nithin Reddy Bathula   12 years AGO

given that he traveled north 300m and then he traveled 200m east. These two make a right angle and then he traveled 300sqrt(2)m southwest.
That means assume that distance traveled for south and north is same i.e, 200m. Applying Pythagoras theorem the hypotenuse distance 200sqrt(2) which means he traveled 100sqrt(2) far. So for the small right angle triangle applying Pythagoras theorem calculate the third side which gives us shortest distance i.e, Ans:100m

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