question_answer

A child was looking for his father. He went 90 metres in the East before turning to his right. He then went 20 metres more before turning to his right again to look for his father at his uncle's place, which was 30 metres from his original point of starting He did not find his father there. So he went 100 metres more towards the 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) 280 m

E) None of these

Correct Answer: B

Solution :

Explanation Option (b) is correct. The movement of the child from A to E are as shown in figure. Finally the child meets his father at E. Now, AF = (90 - 30) m = 60m. EF = (DE - DF) = (DE - BC) = (100 - 20) = 80m. \[\therefore \] Required distance \[=\,AE=\sqrt{{{(AF)}^{2}}+{{(EF)}^{2}}}=\sqrt{{{(60)}^{2}}+{{(80)}^{2}}}=\sqrt{3600+6400}\] \[=\sqrt{10,000}=100m.\]