Three pipes $A, B$ and $C$ can fill a tank in $6$ $hours$. After working together for $2$ $hours$,$C$ is closed and $A$ and $B$ fill the remaining part in $7$ $hours$. The number of $hours$ taken by $C$ alone to fill the tank is?

$A$ tank has two pipes. The first pipe can fill it in $45$ minutes and the second can empty it in $1$ hour. In what time will the empty tank be filled if the pipes are opened one at a time in alternate minutes?

Two pipes $A$ and $B$ can fill a tank in $1$ $h$ and $75$ $min,$ respectively. There is also an outlet $C$. If all the three pipes are opened together, the tank is full in $50$ $min.$ How much time (in $minutes$) will be taken by $C$ to empty the full tank?

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?

An outlet pipe can empty a cistern in $3$ $h$. In what time (in $h$) will the pipe empty two-third part of the cistern?

$A$ 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?