(A) Let the filling capacity of the pump be $x m^3/min$.The emptying capacity of the pump is $(x + 10) m^3/min$.The time taken to fill the tank is $T_

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(A) Let the filling capacity of the pump be $x m^3/min$.The emptying capacity of the pump is $(x + 10) m^3/min$.The time taken to fill the tank is $T_f = \frac{2400}{x}$ minutes.The time taken to empty the tank is $T_e = \frac{2400}{x+10}$ minutes.According to the problem,$T_f - T_e = 8$.$\frac{2400}{x} - \frac{2400}{x+10} = 8$Divide by $8$: $\frac{300}{x} - \frac{300}{x+10} = 1$$300(x + 10) - 300x = x(x + 10)$$300x + 3000 - 300x = x^2 + 10x$$x^2 + 10x - 3000 = 0$$(x + 60)(x - 50) = 0$Since capacity cannot be negative,$x = 50$.Thus,the filling capacity of the pump is $50 m^3/min$.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Medium

$A$ booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is $2400 m^3$. The emptying capacity of the tank is $10 m^3/min$ higher than its filling capacity and the pump needs $8$ minutes less to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A
$50 m^3/min$
B
$60 m^3/min$
C
$72 m^3/min$
D
$32 m^3/min$

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Pipes and Cistern

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Pipes and Cistern

Pipes $A$ and $B$ can fill a tank in $5$ $hours$ and $6$ $hours$ respectively. Pipe $C$ can empty it in $12$ $hours.$ If all the three pipes are opened together,then the tank will be filled in

Medium

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$A$ water tank has three taps $A, B, C$. Tap $A$,when opened,can fill the water tank alone in $4$ hours. Tap $B$,when opened,can fill the water tank alone in $6$ hours,and tap $C$,when opened,can empty the water tank alone in $3$ hours. If taps $A, B,$ and $C$ are opened simultaneously,how long (in hours) will it take to fill the tank completely?

Medium

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$A$ cistern has three pipes $A, B$ and $C$. Pipes $A$ and $B$ can fill it in $3 \, h$ and $4 \, h$, respectively, while pipe $C$ can empty the completely filled cistern in $1 \, h$. If pipes are opened in order at $3:00 \, pm$, $4:00 \, pm$ and $5:00 \, pm$, respectively, at what time will the cistern be empty?

Medium

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$A$ pipe can fill a tank with thrice the speed of another pipe. If both the pipes together take $36$ $min$ to fill an empty tank completely,then how much time will it take for the slower pipe to fill the tank alone?

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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Pipes $A$ and $B$ can fill a tank in $5$ $hours$ and $6$ $hours$ respectively. Pipe $C$ can empty it in $12$ $hours.$ If all the three pipes are opened together,then the tank will be filled in

$A$ pipe can fill a tank with thrice the speed of another pipe. If both the pipes together take $36$ $min$ to fill an empty tank completely,then how much time will it take for the slower pipe to fill the tank alone?

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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