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(C) Let the time taken by pipe $A$ be $X = 12 	ext{ hours}$ and by pipe $B$ be $Y = 15 	ext{ hours}$.The part of the cistern emptied by pipe $A$ in

Vedclass · Accepted Answer

$6 	ext{ hours } 40 	ext{ minutes}$

Vedclass · Answer

(C) Let the time taken by pipe $A$ be $X = 12 	ext{ hours}$ and by pipe $B$ be $Y = 15 	ext{ hours}$.The part of the cistern emptied by pipe $A$ in $1 	ext{ hour}$ is $\frac{1}{12}$.The part of the cistern emptied by pipe $B$ in $1 	ext{ hour}$ is $\frac{1}{15}$.When both pipes are opened together,the part of the cistern emptied in $1 	ext{ hour}$ is $\left(\frac{1}{12} + \frac{1}{15}ight) = \frac{5+4}{60} = \frac{9}{60} = \frac{3}{20}$.Therefore,the total time taken to empty the cistern is the reciprocal of the work done in $1 	ext{ hour}$,which is $\frac{20}{3} 	ext{ hours}$.$\frac{20}{3} 	ext{ hours} = 6 	ext{ hours } + \frac{2}{3} 	imes 60 	ext{ minutes} = 6 	ext{ hours } 40 	ext{ minutes}$.

Two pipes $A$ and $B$ can separately empty a cistern in $12$ $hours$ and $15$ $hours$,respectively. In what time will the cistern be emptied,if both the pipes are opened together?

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