(B) Let the capacity of the cistern be the $LCM$ of $3, 4,$ and $5$, which is $60 \, \text{units}$.Efficiency of the first tap $(A) = \frac{60}{3} = 2

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(B) Let the capacity of the cistern be the $LCM$ of $3, 4,$ and $5$, which is $60 \, \text{units}$.Efficiency of the first tap $(A) = \frac{60}{3} = 20 \, \text{units/h}$.Efficiency of the second tap $(B) = \frac{60}{4} = 15 \, \text{units/h}$.Efficiency of the third tap $(C) = -\frac{60}{5} = -12 \, \text{units/h}$ (since it empties the cistern).When all three taps are opened simultaneously, the net efficiency $= 20 + 15 - 12 = 23 \, \text{units/h}$.Time taken to fill the cistern $= \frac{\text{Total Capacity}}{\text{Net Efficiency}} = \frac{60}{23} \, h$.Converting this to a mixed fraction, we get $2 \frac{14}{23} \, h$.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Medium

Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in $3 \, h$ and $4 \, h$, respectively. The full cistern is emptied by the third tap in $5 \, h$. If all three taps are opened simultaneously, the empty cistern will be filled up in?

A
$1 \frac{14}{23} \, h$
B
$2 \frac{14}{23} \, h$
C
$2 \, h \, 40 \, min$
D
$1 \, h \, 56 \, min$

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Pipes and Cistern

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Pipes and Cistern

Two taps $A$ and $B$ can fill a tank in $25$ $min$ and $20$ $min$ respectively. However,the taps are not opened properly,so taps $A$ and $B$ allow only $\frac{5}{6}$ and $\frac{2}{3}$ of their normal water flow,respectively. How long will they take to fill the tank (in $min$)?

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Three pipes $A, B$ and $C$ can fill a tank in $30 \ min$,$20 \ min$ and $10 \ min$,respectively. When the tank is empty,all the three pipes are opened. If $A, B$ and $C$ discharge chemical solutions $P, Q$ and $R$ respectively,then the part of solution $R$ in the liquid in the tank after $3 \ min$ is

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Two pipes,$A$ and $B,$ can separately fill a cistern in $15$ $minutes$ and $18$ $minutes,$ respectively,while a third pipe $C$ can empty it in $6$ $minutes.$ Two pipes,$A$ and $B,$ are kept open for $6$ $minutes$ in the beginning and,then the third pipe is also opened. In what time (in $minutes$) will the cistern be emptied?

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$A$ water tank is $\frac{2}{3}$ full. Pipe $A$ can fill the tank in $10$ $minutes$ and pipe $B$ can empty it in $6$ $minutes$. If both the pipes are open,how long will it take to empty the tank completely?

Medium

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Two pipes,$A$ and $B,$ can separately fill a tank in $6$ $hours$ and $8$ $hours,$ respectively. Both the pipes are opened together,but $1 \frac{1}{2}$ $hours$ later pipe $A$ is turned off. How much time (in $hours$) will it take to fill the tank?

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Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in $3 \, h$ and $4 \, h$, respectively. The full cistern is emptied by the third tap in $5 \, h$. If all three taps are opened simultaneously, the empty cistern will be filled up in?

Similar Questions

Two taps $A$ and $B$ can fill a tank in $25$ $min$ and $20$ $min$ respectively. However,the taps are not opened properly,so taps $A$ and $B$ allow only $\frac{5}{6}$ and $\frac{2}{3}$ of their normal water flow,respectively. How long will they take to fill the tank (in $min$)?

$A$ water tank is $\frac{2}{3}$ full. Pipe $A$ can fill the tank in $10$ $minutes$ and pipe $B$ can empty it in $6$ $minutes$. If both the pipes are open,how long will it take to empty the tank completely?

Two pipes,$A$ and $B,$ can separately fill a tank in $6$ $hours$ and $8$ $hours,$ respectively. Both the pipes are opened together,but $1 \frac{1}{2}$ $hours$ later pipe $A$ is turned off. How much time (in $hours$) will it take to fill the tank?

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