Two taps can fill a tank in $20$ $min$ and $30$ $min$ respectively. When the tank was empty,both the taps were opened,and after some time,the first tap was closed. It took $18$ $min$ in total to fill the tank. After how much time (in $minutes$) from the beginning was the first tap closed?

$A$ tank can be filled by pipe $A$ in $2$ $hours$ and pipe $B$ in $6$ $hours.$ At $10 \, am$ pipe $A$ was opened. At what time will the tank be filled if pipe $B$ is opened at $11 \, am$?

Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in $3 \, h$ and $4 \, h$, respectively. The full cistern is emptied by the third tap in $5 \, h$. If all three taps are opened simultaneously, the empty cistern will be filled up in?

Two pipes can fill a tank in $20$ $minutes$ and $24$ $minutes$ respectively,and a waste pipe can empty $3$ $gallons$ per minute. All the three pipes working together can fill the tank in $15$ $minutes$. The capacity of the tank is (in $gallons$):

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

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?