$A$ tap can fill a cistern in $40$ $min$ and a second tap can empty the filled cistern in $60$ $min$. By mistake, without closing the second tap, the first tap was opened. In how many $minutes$ will the empty cistern be filled?

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in $36$ minutes,then the slower pipe alone will be able to fill the tank in (in 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 $minutes$)

$A$ tap can fill the cistern in $8$ hours and another can empty it in $16$ hours. If both the taps are opened simultaneously,the time (in hours) to fill the tank is?

If two pipes function simultaneously,the reservoir will be filled in $6$ $hours$. One pipe fills the reservoir $5$ $hours$ faster than the other. How many hours does the faster pipe take to fill the reservoir?

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?