$A$ reservoir is fitted with two pipes $A$ and $B$. Pipe $A$ can fill the reservoir $5$ $hours$ faster than pipe $B$. If both the pipes together fill the reservoir in $6$ $hours$,the reservoir will be filled by $A$ alone in:

$A$ pipe can empty a cistern in $27$ $hours$. Find the time (in $hours$) in which $\frac{2}{3}$ part of the cistern will be emptied?

$A$ pipe $P$ can fill a tank in $12$ $min$ and another pipe $R$ can fill it in $15$ $min.$ But,the $3$rd pipe $M$ can empty it in $6$ $min.$ The $1$st two pipes $P$ and $R$ are kept open for $5$ $min$ in the beginning and then the $3$rd pipe is also opened. In what time (in minutes) is the tank emptied?

Pipe $A$ can fill a tank in $5$ $hours$,pipe $B$ in $10$ $hours$,and pipe $C$ in $30$ $hours$. If all the pipes are opened,in how many $hours$ will the tank be filled?

$A$ pipe can fill a tank with water in $3 \, h$. Due to a leak at the bottom,it takes $3 \frac{1}{2} \, h$ to fill it. In what time (in $hours$) will the leak empty the fully filled tank?

$A$ cistern has $3$ pipes $A, B$ and $C$. Pipes $A$ and $B$ can fill it in $3$ and $4$ hours respectively,and pipe $C$ can empty it in $1$ hour. If the pipes are opened at $3 \text{ pm}$,$4 \text{ pm}$,and $5 \text{ pm}$ respectively on the same day,at what time will the cistern be empty?