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

Options

A. 80 metres
B. 100 metres
C. 140 metres
D. 260 metres

Answer

B

Explanation

The movements of the child are as shown in Fig. i.e. P to Q, Q to R, R to S and S to T.

P = Starting Point T = End Point
So, the child meets his father at T.
PU= (PQ - UQ) = (PQ - RS) = (90 - 30) m = 60 m.
TU= (ST-SU) = (ST- QR) = (100-20) m = 80 m
Therefore, the required distance = PT
`=sqrt(PU^2+TU^2)=sqrt((60)^2+(80)^2)`
`=sqrt(3600+6400)`
`=sqrt(10000)=100m`