Three taps $A, B$ and $C$ together can fill an empty cistern in $10$ $min.$ The tap $A$ alone can fill it in $30$ $min$ and the tap $B$ alone can fill it in $40$ $min.$ How long will the tap $C$ alone take to fill it? (in $minutes$)

$A$ 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?

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.

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:

Two pipes $A$ and $B$ can fill a cistern in $15$ and $20$ $min$,respectively. Both the pipes are opened together,but after $2$ $min$,pipe $A$ is turned off. What is the total time (in $minutes$) required to fill the tank?

An empty tank can be filled by pipe $A$ in $4$ $h$ and by pipe $B$ in $6$ $h$. If the two pipes are opened for $1$ $h$ each alternately,starting with pipe $A$,then in how much time will the tank be filled?