$A$ 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?

$A$ tank has a leak which would empty it in $8$ $hrs$. $A$ tap is turned on which admits $6$ $litres$ a minute into the tank,and it is now emptied in $12$ $hrs$. How many litres does the tank hold?

Two pipes $A$ and $B$ can fill a cistern in $18$ $minutes$ and $9$ $minutes$ respectively,while a third pipe $C$ can empty the full tank in $5$ $minutes$. $A$ and $B$ are kept open for $4$ $minutes$ in the beginning and then $C$ is also opened. In what time (in $minutes$) is the cistern emptied?

Three taps $P, Q$ and $R$ separately can fill a tank completely in $4, 8$ and $12$ hours respectively. Another tap $S$ can empty the filled tank in $10$ hours. Which of the following combinations will fill the empty tank in the least amount of time?

$A$ cistern has two pipes. One can fill it in $8 \, h$ and the other can empty it in $5 \, h$. In how many $hours$ will the cistern be emptied if both the pipes are opened together when $\frac{3}{4}$ of the cistern is already full of water?

Two pipes,$A$ and $B,$ can separately fill a tank in $6$ $hours$ and $8$ $hours,$ respectively. Both the pipes are opened together,but $1 \frac{1}{2}$ $hours$ later pipe $A$ is turned off. How much time (in $hours$) will it take to fill the tank?