Two pipes $A$ and $B$ can fill a cistern in $3$ $hours$ and $5$ $hours,$ respectively. Pipe $C$ can empty it in $2$ $hours.$ If all the three pipes are open,in how many $hours$ will the cistern be full?

$A$ tap can fill a cistern in $8$ $hours$ and another can empty it in $16$ $hours$. If both the taps are opened simultaneously,the time (in $hours$) to fill the tank is?

Two pipes $A$ and $B$ can fill a tank in $24$ and $32$ $min$,respectively. If both the pipes are opened together,after how much time pipe $B$ should be closed so that the tank is full in $9$ $min$ (in $min$)?

If pipe $P$ can fill a tank in $p$ hours and pipe $Q$ can empty the same tank in $q$ hours (where $q > p$),and both pipes are opened simultaneously,in how many hours $(r)$ will the tank be filled?

$A$ pipe can fill a cistern in $4$ $min$ and another pipe can fill it in $5$ $min,$ but a third pipe can empty it in $2$ $min.$ The first two pipes are kept open for $2$ $min$ in the beginning and then the third pipe is also opened. Time (in $min$) taken to empty the cistern is?

Pipe $X$ can fill a tank in $20$ $hours$ and pipe $Y$ can fill the tank in $35$ $hours.$ Both the pipes are opened on alternate hours. Pipe $Y$ is opened first,then in how much time (in hours) will the tank be full?