Two pipes $A$ and $B$ can fill a cistern in $37 \frac{1}{2}$ minutes and $45$ minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour,if pipe $B$ is turned off after how many minutes?

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?

$A$ tank is filled in $5$ $hours$ by three pipes $A, B$ and $C$. The pipe $C$ is twice as fast as $B$ and $B$ is twice as fast as $A$. How much time (in $hours$) will pipe $A$ alone take to fill the tank?

Two pipes can fill a cistern in $14$ $h$ and $16$ $h$,respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom,it took $92$ $min$ more to fill the cistern. When the cistern is full,in what time will the leak empty it?

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?

Three taps $A, B$ and $C$ can fill a tank in $12, 15$ and $20$ hours respectively. If $A$ is open all the time and $B$ and $C$ are open for one hour each alternately,the tank will be full in? (in hours)