$A$ tap can fill a tank in $25$ $minutes$ and another can empty it in $50$ $minutes$. Find out whether the tank will be filled up or emptied and in how many $minutes$?

$A$ cistern is filled by two taps $A$ and $B$. Tap $A$ can fill it in $20$ $minutes$ and tap $B$ in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second tap $(B)$ is turned off. The cistern will be completely filled in another:

Three pipes $A, B$ and $C$ can fill a tank from empty to full in $30$ minutes,$20$ minutes and $10$ minutes respectively. When the tank is empty,all the three pipes are opened. $A, B$ and $C$ discharge chemical solutions $P, Q$ and $R$ respectively. What is the proportion of solution $R$ in the liquid in the tank after $3$ minutes?

Having the same capacity,$9$ taps fill up a water tank in $20$ minutes. How many taps of the same capacity are required to fill up the same water tank in $15$ minutes?

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 $minutes$)

Two taps $A$ and $B$ can fill an oil tank in $15$ $min$ and $18$ $min$ respectively,while a third tap is used to empty the tank. The third tap is opened after $6$ $min$ of opening of taps $A$ and $B$. If the tank empties in $16 \frac{1}{2}$ $min$ after opening the third tap,then in how much time (in $min$) can the third tap empty the full tank?