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 $U$?

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?

There are four towns $P, Q, R$ and $T$. $Q$ is to the South-west of $P$,$R$ is to the East of $Q$ and South-east of $P$,and $T$ is to the North of $R$ in line with $QP$. In which direction of $P$ is $T$ located?

Two buses start from the opposite points of a main road,$150 \, km$ apart. The first bus runs for $25 \, km$ and takes a right turn and then runs for $15 \, km$. It then turns left and runs for another $25 \, km$ and takes the direction back to reach the main road. In the meantime,due to a minor breakdown,the other bus has run only $35 \, km$ along the main road. What would be the distance between the two buses at this point? (in $km$)

$A$ 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?

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