question_answer

A child is looking for his father. He went 90 m in the East before turning to his right. He went 20 m before turning to his right again to look for his father at his uncle's place 30 m from this point. His father was not there. From there, he went 100 m to his North before meeting his father in a street. How far did the son meet his father from the starting point?

A) 80 m               

B) 100 m

C) 140 m             

D) 260 m

Correct Answer: B

Solution :

Clearly, the child moves form A, 90 m eastwards upto B then turns right and moves 20 m upto C, then turns right am moves 30 m upto D. Finally, he turns right and moves 100 m upto E. Clearly,             \[AB=90\,\,m,\,\,BF=CD=30\,\,m\] So        \[AF=AB-BF=60\,\,m\] Also,     \[DE=100\,\,m,\,\,DF=BC=20\,\,m\] So,       \[EF=DE-DF=80\,\,m\] \[\therefore \]His distance from starting point A             \[=AE=\sqrt{A{{F}^{2}}+E{{F}^{2}}}\]             \[=\sqrt{{{(60)}^{2}}+{{(80)}^{2}}}=\sqrt{3600+6400}\]             \[=\sqrt{10000}=100\,\,m\]