Two pipes A and B can fill a tank in 30 minut | vedclass

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(D) $1$. Calculate the efficiency of each pipe by finding the Least Common Multiple $(LCM)$ of $30, 45,$ and $36$,which is $180$ units.$2$. Efficiency

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(D) $1$. Calculate the efficiency of each pipe by finding the Least Common Multiple $(LCM)$ of $30, 45,$ and $36$,which is $180$ units.$2$. Efficiency of $A = 180 / 30 = 6$ units/min.$3$. Efficiency of $B = 180 / 45 = 4$ units/min.$4$. Efficiency of $C = -180 / 36 = -5$ units/min (negative because it empties).$5$. Pipes $A$ and $B$ work together for $12$ minutes: $(6 + 4) 	imes 12 = 10 	imes 12 = 120$ units.$6$. Remaining work to be filled $= 180 - 120 = 60$ units.$7$. When $C$ is opened,the combined efficiency becomes $A + B + C = 6 + 4 - 5 = 5$ units/min.$8$. Time taken to fill the remaining $60$ units $= 60 / 5 = 12$ minutes.$9$. 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 full 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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