question_answer

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 the destination is

A)  12 km             

B)  15 km

C)  16 km             

D)  18 km

Correct Answer: B

Solution :

The movements of the person are as shown in figure Clearly, \[AB=3\,km,\]             \[BC=3AB=(3\times 3)km\]                   \[=9\,km\]             \[CD=5AB=(5\times 3)km\]                   \[=5\,km\] Draw \[AE\bot CD\] Then, \[CE=AB=3\text{ }km\] and \[AE=BC=9\,km\] \[DE=(CD-CE)=(15-3)\,km=12\,\,km\] In \[\Delta AED,\] \[A{{D}^{2}}=A{{E}^{2}}+D{{E}^{2}}\] \[\Rightarrow \]   \[AD=\sqrt{{{9}^{2}}+{{(12)}^{2}}}km=\sqrt{225}\,\,km\] \[=15\,\,km\] \[\therefore \] Required distance \[=AD=15\,km\]