Two pipes can fill an empty tank separately in $24$ $minutes$ and $40$ $minutes$ respectively,and a third pipe can empty $30$ $gallons$ of water per $minute$. If all three pipes are opened,the empty tank becomes full in one $hour$. The capacity of the tank (in $gallons$) 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 $min$)?

$A$ pipe can empty a cistern in $27$ $hours$. Find the time (in $hours$) in which $\frac{2}{3}$ part of the cistern will be emptied?

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?

In what time would a cistern be filled by three pipes whose diameters are $1 \text{ cm}$,$1 \frac{1}{3} \text{ cm}$,and $2 \text{ cm}$,running together,when the largest alone will fill it in $61 \text{ minutes}$,the amount of water flowing in by each pipe being proportional to the square of its diameter? (in $\text{minutes}$)

Two taps can fill a tank in $20$ $min$ and $30$ $min$ respectively. When the tank was empty,both the taps were opened,and after some time,the first tap was closed. It took $18$ $min$ in total to fill the tank. After how much time (in $minutes$) from the beginning was the first tap closed?