$12$ 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?

$A$ cistern can be filled by two pipes $A$ and $B$ in $4$ $hours$ and $6$ $hours$ respectively. When full,the tank can be emptied by a third pipe in $8$ $hours$. If all the taps are turned on at the same time,the cistern will be full in?

Two taps $A$ and $B$ can fill a tank in $25$ $min$ and $20$ $min$ respectively. However,the taps are not opened properly,so taps $A$ and $B$ allow only $\frac{5}{6}$ and $\frac{2}{3}$ of their normal water flow,respectively. How long will they take to fill the tank (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?

If two pipes function simultaneously,the reservoir will be filled in $6$ $hours$. One pipe fills the reservoir $5$ $hours$ faster than the other. How many $hours$ does the faster pipe take to fill the reservoir?

Two pipes $A$ and $B$ can fill a cistern in $24$ $minutes$ and $30$ $minutes$,respectively. There is also an outlet $C$. If all the three pipes are opened together,the cistern is full in $20$ $minutes$. How much time (in $minutes$) will be taken by outlet $C$ to empty the full cistern?