$A$ man leaves for his office from his house. He walks towards East. After moving a distance of $20 \,m,$ he turns towards South and walks $10 \,m.$ Then he walks $35 \,m$ towards the West and further $5 \,m$ towards the North. He then turns towards East and walks $15 \,m.$ What is the straight distance in metres between his initial and final positions?

Six flats on a floor in two rows facing North and South are allotted to $P, Q, R, S, T$ and $U$.
$(i)$ $Q$ gets a North-facing flat and is not next to $S$.
(ii) $S$ and $U$ get diagonally opposite flats.
(iii) $R$,next to $U$,gets a South-facing flat and $T$ gets a North-facing flat.
Which of the other pairs,besides $SU$,are diagonally opposite to each other?

After walking a distance of $50 \, m$ to the south of her house,Lakshmi turns left and walks another $20 \, m$. Then she turns north and walks $30 \, m$ and then starts walking to her house. In which direction is she walking now?

Dinesh walks $20 \,m$ north. Then he turns right and walks $30 \,m$. Now he turns right and walks $35 \,m$. Now, turning left, he walks $15 \,m$. Again, he turns left and moves $15 \,m$. Finally, turning left, he again walks $15 \,m$. In which direction and how far is he from his original position?

$A$ 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? (in $m$)

$A$ and $B$ start moving towards each other from two places $200 \,m$ apart. After walking $60 \,m$,$B$ turns left and goes $20 \,m$,then he turns right and goes $40 \,m$. He then turns right again and comes back to the road on which he had started walking. If $A$ and $B$ walk with the same speed,what is the distance between them now? (in $m$)