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(B) Let the total capacity of the tank be the $LCM$ of $30, 45,$ and $36$,which is $180$ units.Efficiency of $A = 180 / 30 = 6$ units/min.Efficiency o

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$24$

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(B) Let the total capacity of the tank be the $LCM$ of $30, 45,$ and $36$,which is $180$ units.Efficiency of $A = 180 / 30 = 6$ units/min.Efficiency of $B = 180 / 45 = 4$ units/min.Efficiency of $C = 180 / 36 = -5$ units/min (since it empties the tank).In the first $12$ minutes,$A$ and $B$ work together: $(6 + 4) 	imes 12 = 10 	imes 12 = 120$ units filled.Remaining capacity to be filled $= 180 - 120 = 60$ units.After $12$ minutes,$C$ is opened,so all three pipes work together: Efficiency $= 6 + 4 - 5 = 5$ units/min.Time taken to fill the remaining $60$ units $= 60 / 5 = 12$ minutes.Total time taken $= 12$ (initial) $+ 12$ (remaining) $= 24$ minutes.

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?

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