$A$ clock gaining $2 \, \text{minutes}$ every hour was synchronized at midnight with a clock losing $1 \, \text{minute}$ every hour. How many minutes behind will the second clock be at $11:00 \, \text{AM}$ the following morning compared to the clock gaining $2 \, \text{minutes}$ every hour?

Laxman went $15 \, km$ to the west from my house,then turned left and walked $20 \, km$. He then turned east and walked $25 \, km$ and finally turning left,covered $20 \, km$. How far was he from my house? (in $\, km$)

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?

$A$ man walked $30 \, m$ towards south. Then,he turned to his right and walked $30 \, m$. Then,he turned to his left and walked $20 \, m$. Again,he turned to his left and walked $30 \, m$. How far is he from his initial position?

$A$ 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 $U$?