$A$ man walks $6 \, km$ to the east and then turns to the south and walks $5 \, km$. Again he turns to the east and walks $6 \, km$. Next,he turns towards north and walks $10 \, km$. How far is he now from his starting point (in $, km$)?

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.
If the flats of $T$ and $P$ are interchanged,whose flat will be next to that of $U$?

Rohit walked $25 \, m$ towards South. Then he turned to his left and walked $20 \, m$. He then turned to his left and walked $25 \, m$. He again turned to his right and walked $15 \, m$. At what distance is he from the starting point and in which direction?

The post office is to the east of the school,while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school,in which direction is the market with respect to my school?

Kashish goes $30 \, m$ North,then turns right and walks $40 \, m$,then again turns right and walks $20 \, m$,then again turns right and walks $40 \, m$. How many metres is he from his original position?

$A$ postman was returning to the Post Office,which was in front of him to the north. When the Post Office was $100 \, m$ away from him,he turned to the left and moved $50 \, m$ to deliver the last letter at Shanti Villa. He then moved in the same direction for $40 \, m$,turned to his right,and moved $100 \, m$. How many metres away was he now from the Post Office? (in $m$)