$A$ tank can be filled by one tap in $20$ $minutes$ and by another in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second is turned off. In how many $minutes$ more will the tank be completely filled?

Two pipes $A$ and $B$ can fill a tank in $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

$A$ tank can be filled by one tap in $20$ $min$ and by another tap in $60$ $min$. Both the taps are kept open for $5$ $min$ and then the $1$st tap is shut off. After this,how much more time (in $min$) will it take for the tank to be completely filled?

$A$ 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?

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?

$A$ pipe $P$ can fill a tank in $12$ $min$ and another pipe $R$ can fill it in $15$ $min.$ But,the $3$rd pipe $M$ can empty it in $6$ $min.$ The $1$st two pipes $P$ and $R$ are kept open for $5$ $min$ in the beginning and then the $3$rd pipe is also opened. In what time (in minutes) is the tank emptied?