$A$ pipe can fill a tank in $x$ $h$ and another pipe can empty it in $y$ $(y > x)$ $h.$ If both the pipes are open,in how many hours will the tank be filled?

Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)

$A$ cistern is filled by two taps $A$ and $B$. Tap $A$ can fill it in $20$ $minutes$ and tap $B$ in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second tap $(B)$ is turned off. The cistern will be completely filled in another:

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 $min$)?

$A$ water tank has three taps $A, B, C$. Tap $A$,when opened,can fill the water tank alone in $4$ hours. Tap $B$,when opened,can fill the water tank alone in $6$ hours,and tap $C$,when opened,can empty the water tank alone in $3$ hours. If taps $A, B,$ and $C$ are opened simultaneously,how long (in hours) will it take to fill the tank completely?

$A$ tap can fill a cistern in $40$ $min$ and a second tap can empty the filled cistern in $60$ $min$. By mistake, without closing the second tap, the first tap was opened. In how many $minutes$ will the empty cistern be filled?