question_answer

A villager went to meet his uncle in another village situated 5 km away in the North-East direction of his own village. From there he came to meet his father-in-law living in a village situated 4 km in the South of his uncle's village. How far away and in what direction is he now?

A)  3 km in the North          

B)  3 km in the East

C)  4 km in the East

D)  4 km in the West

Correct Answer: B

Solution :

The villager moves from his village at O to his uncle's village at A and thereon to his father-in-law's village at B. clearly, A ABO is right angled at B. So, \[O{{A}^{2}}=O{{B}^{2}}+A{{B}^{2}}\] \[\Rightarrow \]   \[O{{B}^{2}}=O{{A}^{2}}-A{{B}^{2}}\] \[\Rightarrow \]   \[OB=\sqrt{(25-16)km}\]             \[=(\sqrt{9})km=3km\] Thus, B is 3 km to the East of his initial position O.