Two taps can separately fill a cistern in $10$ $minutes$ and $15$ $minutes$ respectively. When the waste pipe is open,they can together fill it in $18$ $minutes$. The waste pipe can empty the full cistern in:

Two taps $A$ and $B$ can fill a tank in $25$ $min$ and $20$ $min$ respectively. However,the taps are not opened properly,so taps $A$ and $B$ allow only $\frac{5}{6}$ and $\frac{2}{3}$ of their normal water flow,respectively. How long will they take to fill the tank (in $min$)?

Three pipes $A, B$ and $C$ can fill a cistern in $6$ $hrs$. After working together for $2$ $hrs$,$C$ is closed and $A$ and $B$ fill the remaining part of the cistern in $8$ $hrs$. Find the time (in $hrs$) in which the cistern can be filled by pipe $C$ alone.

Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)

Two pipes can fill a cistern separately in $24$ $minutes$ and $40$ $minutes$ respectively. $A$ waste pipe can drain off $30 \text{ litres per minute}$. If all the three pipes are opened,the cistern fills in one $hour$. The capacity (in $litres$) of the cistern is:

$A$ swimming pool is fitted with three pipes. The first two pipes working simultaneously fill the pool in the same time as the third pipe alone. The second pipe alone fills the pool $5$ hours faster than the first pipe and $4$ hours slower than the third pipe. In what time (in hours) will the second and third pipes together fill the pool?