Arun moved a distance of $75 \, m$ towards north. He then turned to the left and walked for about $25 \, m$,turned left again and walked $80 \, m$. Finally,he turned to the right at an angle of $45^{\circ}$. In which direction was he moving finally?

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.
Whose flat is between $Q$ and $S$?

$A$ man walks $30 \,m$ towards South. Then,turning to his right,he walks $30 \,m.$ Then,turning to his left,he walks $20 \,m.$ Again,he turns to his left and walks $30 \,m.$ How far is he from his initial position (in $m$)?

Ravi walked $2 \, km$ west of his house and then turned south,covering $4 \, km$. Finally,he moved $3 \, km$ towards east and then again $1 \, km$ west. How far is he from his initial position (in $, km$)?

Sachin and Vinod want to visit the museum after their exams. Sachin's exams finish on $9^{th}$ April and he is leaving for a holiday on $12^{th}$ April. Vinod's exams will be over by $10^{th}$ April,after which he is free. On which of the following dates can the two definitely meet?

Ravi wants to go to the university. He starts from his home,which is in the East,and comes to a crossing. The road to the left ends in a theatre,and straight ahead is the hospital. In which direction is the university?