(A) Let the rates of the three pipes be $A, B,$ and $C$ respectively.Rate of pipe $A = 1/10$ tank per hour.Rate of pipe $B = 1/12$ tank per hour.Rate

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$7 \text{ hours } 30 \text{ minutes}$

(A) Let the rates of the three pipes be $A, B,$ and $C$ respectively.Rate of pipe $A = 1/10$ tank per hour.Rate of pipe $B = 1/12$ tank per hour.Rate of pipe $C$ (emptying) $= -1/20$ tank per hour.When all three pipes are open simultaneously,the net rate of filling is:$(1/10 + 1/12 - 1/20) \text{ tank per hour}$.Taking the least common multiple $(LCM)$ of $10, 12,$ and $20$,which is $60$:Net rate $= (6/60 + 5/60 - 3/60) = 8/60 = 2/15$ tank per hour.Time taken to fill the tank $= 1 / (2/15) = 15/2 = 7.5$ hours.$7.5$ hours is equal to $7$ hours and $30$ minutes.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Medium

Two pipes can fill a tank in $10$ $hours$ and $12$ $hours,$ while a third pipe can empty the full tank in $20$ $hours.$ If all three pipes operate simultaneously,in how much time will the tank be filled?

A
$7 \text{ hours } 30 \text{ minutes}$
B
$6 \text{ hours } 40 \text{ minutes}$
C
$8 \text{ hours } 30 \text{ minutes}$
D
$\text{None of these}$

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Pipes and Cistern

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Pipes and Cistern

Two pipes $A$ and $B$ can separately fill a cistern in $60$ $minutes$ and $75$ $minutes$ respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened,then the cistern is full in $50$ $minutes$. In how much time (in $minutes$) can the third pipe alone empty the cistern?

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$A$ leak in the bottom of a tank can empty the full tank in $8$ $hours$. An inlet pipe fills water at the rate of $6$ $litres$ a minute. When the tank is full,the inlet pipe is opened and due to the leak,the tank is empty in $12$ $hours$. How many litres does the tank hold?

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Two pipes can fill an empty tank separately in $24$ $minutes$ and $40$ $minutes$ respectively,and a third pipe can empty $30$ $gallons$ of water per $minute$. If all three pipes are opened,the empty tank becomes full in one $hour$. The capacity of the tank (in $gallons$) is:

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Two taps $A$ and $B$ can fill a tank in $20 \text{ min}$ and $30 \text{ min}$,respectively. An outlet pipe $C$ can empty the full tank in $15 \text{ min}$. If $A, B$,and $C$ are opened alternatively,each for $1 \text{ min}$,how long (in $\text{min}$) will the tank take to be filled?

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Two taps $A$ and $B$ can fill a tank in $10$ $hours$ and $12$ $hours$ respectively. If both taps are opened at $10 \text{ am}$,at what time (in $\text{pm}$) should tap $A$ be closed so that the tank is completely filled at exactly $4 \text{ pm}$?

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Two pipes can fill a tank in $10$ $hours$ and $12$ $hours,$ while a third pipe can empty the full tank in $20$ $hours.$ If all three pipes operate simultaneously,in how much time will the tank be filled?

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$A$ leak in the bottom of a tank can empty the full tank in $8$ $hours$. An inlet pipe fills water at the rate of $6$ $litres$ a minute. When the tank is full,the inlet pipe is opened and due to the leak,the tank is empty in $12$ $hours$. How many litres does the tank hold?

Two pipes can fill an empty tank separately in $24$ $minutes$ and $40$ $minutes$ respectively,and a third pipe can empty $30$ $gallons$ of water per $minute$. If all three pipes are opened,the empty tank becomes full in one $hour$. The capacity of the tank (in $gallons$) is:

Two taps $A$ and $B$ can fill a tank in $20 \text{ min}$ and $30 \text{ min}$,respectively. An outlet pipe $C$ can empty the full tank in $15 \text{ min}$. If $A, B$,and $C$ are opened alternatively,each for $1 \text{ min}$,how long (in $\text{min}$) will the tank take to be filled?

Two taps $A$ and $B$ can fill a tank in $10$ $hours$ and $12$ $hours$ respectively. If both taps are opened at $10 \text{ am}$,at what time (in $\text{pm}$) should tap $A$ be closed so that the tank is completely filled at exactly $4 \text{ pm}$?

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