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 $P$ 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?

Two pipes $A$ and $B$ can fill a tank in $15$ $minutes$ and $20$ $minutes$ respectively. Both the pipes are opened together but after $4$ $minutes,$ pipe $A$ is turned off. What is the total time required to fill the tank?

$12$ pumps working $6$ hours a day can empty a completely filled reservoir in $15$ days. How many such pumps working $9$ hours a day will empty the same reservoir in $12$ days?

Two pipes can fill a cistern separately in $24$ $minutes$ and $40$ $minutes$ respectively. $A$ waste pipe can drain off $30 \text{ litres per minute}$. If all the three pipes are opened,the cistern fills in one $hour$. The capacity (in $litres$) of the cistern is:

Two pipes,$A$ and $B,$ can separately fill a cistern in $15$ $minutes$ and $18$ $minutes,$ respectively,while a third pipe $C$ can empty it in $6$ $minutes.$ Two pipes,$A$ and $B,$ are kept open for $6$ $minutes$ in the beginning and,then the third pipe is also opened. In what time (in $minutes$) will the cistern be emptied?