Two taps $A$ and $B$ can fill a tank in $10$ $hours$ and $12$ $hours$ respectively. If both taps are opened at $10 \text{ am}$,at what time (in $\text{pm}$) should tap $A$ be closed so that the tank is completely filled at exactly $4 \text{ pm}$?

One tap can fill a cistern in $2$ $hours$ and another can empty the cistern in $3$ $hours.$ How long will they take to fill the cistern if both the taps are opened?

Two taps $P$ and $Q$ can fill a water tank in $12$ $min$ and $15$ $min$ respectively. They are opened together,but after $3$ $min$,tap $P$ is closed. How much more time will $Q$ take to fill the remaining part of the tank?

If two pipes function together,the tank will be filled in $12$ $h$. One pipe fills the tank $10$ $h$ faster than the other. How many $h$ does the faster pipe take to fill up the tank?

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 $min$)?

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?