$A$ water tank has two taps $A$ and $B$. Tap $A$ can fill it in $6$ hours,and tap $B$ can empty it in $5$ hours. If both taps are opened simultaneously,how much time (in hours) is required to empty the 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?

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?

$18$ pumps can fill a reservoir of capacity $1440 \text{ kilo liter}$ in $5 \text{ hours}$. How many $\text{hours}$ are required to fill a reservoir of capacity $1920 \text{ kilo liter}$ by $8$ pumps?

$A, B, C$ are pipes attached to a cistern. $A$ and $B$ can fill it in $20$ and $30$ minutes respectively,while $C$ can empty it in $15$ minutes. If $A, B, C$ are kept open successively for $1$ minute each,how soon will the cistern be filled? (in minutes)

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)