(B) Let the total capacity of the cistern be the least common multiple of $3, 4,$ and $5$,which is $60$ units.Efficiency of the first tap $= 60 / 3 =

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(B) Let the total capacity of the cistern be the least common multiple of $3, 4,$ and $5$,which is $60$ units.Efficiency of the first tap $= 60 / 3 = 20$ units/h.Efficiency of the second tap $= 60 / 4 = 15$ units/h.Efficiency of the third tap (emptying) $= - (60 / 5) = -12$ units/h.When all three taps are opened simultaneously,the net efficiency $= 20 + 15 - 12 = 23$ units/h.Time taken to fill the cistern $= \text{Total capacity} / \text{Net efficiency} = 60 / 23 \, h = 2 \frac{14}{23} \, h$.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Easy

Three taps are fitted to a cistern. The empty cistern is filled by the first and second taps in $3$ 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 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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$A$ tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank $5$ $hours$ faster than the first pipe and $4$ $hours$ slower than the third pipe. The time (in $hours$) required by the first pipe is:

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$A$ tank has two pipes. The first pipe can fill it in $45$ minutes and the second can empty it in $1$ hour. In what time will the empty tank be filled if the pipes are opened one at a time in alternate minutes?

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$A$ tank has a leak which would empty it in $8$ $hrs$. $A$ tap is turned on which admits $6$ $litres$ a minute into the tank,and it is now emptied in $12$ $hrs$. How many litres does the tank hold?

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$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

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Three taps are fitted to a cistern. The empty cistern is filled by the first and second taps in $3$ 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 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?

$A$ tank has two pipes. The first pipe can fill it in $45$ minutes and the second can empty it in $1$ hour. In what time will the empty tank be filled if the pipes are opened one at a time in alternate minutes?

$A$ tank has a leak which would empty it in $8$ $hrs$. $A$ tap is turned on which admits $6$ $litres$ a minute into the tank,and it is now emptied in $12$ $hrs$. How many litres does the tank hold?

$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

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