question_answer

Four persons stationed at the four corners of a square piece as shown in the diagram. B starts crossing the field diagonally. After walking half the distance, he turns right, walks some distance and turns left. Which direction is B facing now?                                     

A)  North-East                   

B)  South-East

C)  North-West                   

D)  North

Correct Answer: C

Solution :

 : The villager moves from his village at O to his uncle's village at A and then to his brother-in-law's village at B. Clearly, AOBA is right-angled triangle at B.                            So,       \[O{{A}^{2}}=O{{B}^{2}}+A{{B}^{2}}\] \[\Rightarrow O{{B}^{2}}=O{{A}^{2}}-A{{b}^{2}}\] \[OB=\sqrt{(25-16)}km=\sqrt{9}km=3km\] Thus, B is 3 km to the east of his initial position 0.