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:

$A$ cistern can be filled by a tap in $4$ $hours$,while it can be emptied by another tap in $9$ $hours$. If both the taps are opened simultaneously,then after how much time (in $hours$) will the cistern get filled?

Two taps $A$ and $B$ can fill a tank in $10$ $hours$ and $15$ $hours$,respectively. If both the taps are opened together,the tank will be full in (in $hours$):

Two pipes $A$ and $B$ together can fill a cistern in $4$ $hours$. Had they been opened separately,then $B$ would have taken $6$ $hours$ more than $A$ to fill the cistern. How much time (in $hours$) will be taken by $A$ to fill the cistern separately?

$A$ tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank $5$ $hours$ faster than the first pipe and $4$ $hours$ slower than the third pipe. The time (in $hours$) required by the first pipe is:

Three taps $A, B$ and $C$ can fill a tank in $12, 15$ and $20$ hours respectively. If $A$ is kept open all the time,and $B$ and $C$ are opened for one hour each alternately,how long will it take to fill the tank?