Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

$A$ pipe fills a water tank three times faster than another pipe. If the two pipes together can fill the empty tank in $36$ $minutes$,then how much time will the slower pipe alone take to fill the tank?

Two pipes can separately fill a tank in $20$ $hrs$ and $30$ $hrs$ respectively. Both the pipes are opened to fill the tank,but when the tank is $\frac{1}{3}$ full,a leak develops in the tank through which $\frac{1}{3}$ of the water supplied by both the pipes per hour leaks out. What is the total time (in $hrs$) taken to fill the tank?

Pipe $A$ can fill an empty tank in $6$ $hours$ and pipe $B$ in $8$ $hours$. If both the pipes are opened and after $2$ $hours$ pipe $A$ is closed,how much time will pipe $B$ take to fill the remaining tank?

Two pipes $A$ and $B$ can fill a tank in $37 \frac{1}{2}$ minutes and $45$ minutes respectively. If both pipes are opened together,after how much time (in minutes) should pipe $B$ be closed so that the tank is full in exactly $30$ minutes?

Pipes $P$ and $Q$ can fill a tank in $10$ and $12$ $h$, respectively, and pipe $C$ can empty it in $6$ $h$. If all the three are opened at $7$ $am$, at what time will one-fourth of the tank be filled?