A cistern can be filled by two pipes A and B | vedclass

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(B) The part of the tank filled by pipe $A$ in $1 	ext{ hour}$ is $\frac{1}{4}$.The part of the tank filled by pipe $B$ in $1 	ext{ hour}$ is $\frac

Vedclass · Accepted Answer

$3 \frac{3}{7} 	ext{ hrs}$

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(B) The part of the tank filled by pipe $A$ in $1 	ext{ hour}$ is $\frac{1}{4}$.The part of the tank filled by pipe $B$ in $1 	ext{ hour}$ is $\frac{1}{6}$.The part of the tank emptied by pipe $C$ in $1 	ext{ hour}$ is $\frac{1}{8}$.When all three pipes are opened simultaneously,the net part of the tank filled in $1 	ext{ hour}$ is $\frac{1}{4} + \frac{1}{6} - \frac{1}{8}$.Taking the least common multiple $(LCM)$ of $4, 6,$ and $8$,which is $24$:Net part filled in $1 	ext{ hour} = \frac{6 + 4 - 3}{24} = \frac{7}{24}$.Therefore,the total time required to fill the cistern is the reciprocal of the net part filled per hour:$	ext{Time} = \frac{24}{7} = 3 \frac{3}{7} 	ext{ hours}$.

$A$ cistern can be filled by two pipes $A$ and $B$ in $4$ $hours$ and $6$ $hours$ respectively. When full,the tank can be emptied by a third pipe in $8$ $hours$. If all the taps are turned on at the same time,the cistern will be full in?

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