A cistern has 3 pipes A, B and C. Pipes A and | vedclass

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(A) Let the total capacity of the cistern be the $LCM$ of $3, 4,$ and $1$,which is $12$ units.Efficiency of pipe $A = +4$ units/hour.Efficiency of pip

Vedclass · Accepted Answer

$7:12 	ext{ pm}$

Vedclass · Answer

(A) Let the total capacity of the cistern be the $LCM$ of $3, 4,$ and $1$,which is $12$ units.Efficiency of pipe $A = +4$ units/hour.Efficiency of pipe $B = +3$ units/hour.Efficiency of pipe $C = -12$ units/hour.Pipe $A$ is opened at $3 	ext{ pm}$. By $5 	ext{ pm}$,it has worked for $2$ hours. Work done $= 2 	imes 4 = 8$ units.Pipe $B$ is opened at $4 	ext{ pm}$. By $5 	ext{ pm}$,it has worked for $1$ hour. Work done $= 1 	imes 3 = 3$ units.Total work done by $5 	ext{ pm} = 8 + 3 = 11$ units.At $5 	ext{ pm}$,all three pipes are open. Net efficiency $= 4 + 3 - 12 = -5$ units/hour.This means the cistern is being emptied at a rate of $5$ units/hour.Time taken to empty the $11$ units $= \frac{11}{5} 	ext{ hours} = 2 	ext{ hours and } 12 	ext{ minutes}$.Therefore,the cistern will be empty at $5 	ext{ pm} + 2 	ext{ hours } 12 	ext{ minutes} = 7:12 	ext{ pm}$.

$A$ cistern has $3$ pipes $A, B$ and $C$. Pipes $A$ and $B$ can fill it in $3$ and $4$ hours respectively,and pipe $C$ can empty it in $1$ hour. If the pipes are opened at $3 \text{ pm}$,$4 \text{ pm}$,and $5 \text{ pm}$ respectively on the same day,at what time will the cistern be empty?

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