question_answer

Rajan moves 20 km towards North. From there he moves 16 km towards south, then he moves 3 km towards East. How far and in which direction is he with reference to his starting point?

A) 8 km West                    

B) 5 km North-East

C) 7 km West                    

D) 6 km North-East

Correct Answer: B

Solution :

Let A be the starting point. So, In above diagram - \[AB=AC-BC\text{ }\Rightarrow \text{ }AB=20-16=4\text{ }km\] and \[BD=3\text{ }km\text{ }\Rightarrow \]So,. In \[\Delta \,ABD\] \[AD=\sqrt{A{{B}^{2}}+B{{D}^{2}}}\] [By applying Pythagoras theorem] \[AD=\sqrt{{{4}^{2}}+{{3}^{2}}}\Rightarrow AD=\sqrt{25}=AD=5\,km\] So, Rajan's distance from starting point is 5 km and he is in North-East direction.