Question

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

• A. $80m$
• B. $100m$
• C. $140m$
• D. $260m$

Answer 1

The correct option is B $100m$

The movements of the child from $A$ to $E$ are as shown in fig
Clearly, the child meets his father at $E$.
Now $AF=(AB-FB)=(AB-DC)=(90-30)m=60m$.
$EF=(DE-DF)=(DE-BC)=(100-20)m=80m$.
$\therefore$ Required distance
$=AE=\sqrt{A{F}^2+E{F}^2}=\sqrt{(60{)}^2+(80{)}^2)}$
$=\sqrt{3600+6400}=\sqrt{10000}=100m$