(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 $P$ and $Q$ can fill a tank in $10$ and $12$ $h$, respectively, and pipe $C$ can empty it in $6$ $h$. If all the three are opened at $7$ $am$, at what time will one-fourth of the tank be filled?

Medium

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

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Three taps $P, Q$ and $R$ separately can fill a tank completely in $4, 8$ and $12$ hours respectively. Another tap $S$ can empty the filled tank in $10$ hours. Which of the following combinations will fill the empty tank in the least amount of time?

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Two pipes $A$ and $B$ can fill a tank in $15$ hours and $20$ hours respectively,while a third pipe $C$ can empty the full tank in $25$ hours. All three pipes are opened in the beginning. After $10$ hours,pipe $C$ is closed. Find the total time (in hours) in which the tank will be full.

Medium

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Three pipes $A, B$ and $C$ can fill a tank in $6$ $hours$. After running them together for $2$ $hours$, the tap $C$ is closed and $A$ and $B$ fill the remaining part in $7$ $hours$. How much time (in $hours$) would $C$ take to fill the tank alone?

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Pipes $P$ and $Q$ can fill a tank in $10$ and $12$ $h$, respectively, and pipe $C$ can empty it in $6$ $h$. If all the three are opened at $7$ $am$, at what time will one-fourth of the tank be filled?

Three taps $P, Q$ and $R$ separately can fill a tank completely in $4, 8$ and $12$ hours respectively. Another tap $S$ can empty the filled tank in $10$ hours. Which of the following combinations will fill the empty tank in the least amount of time?

Two pipes $A$ and $B$ can fill a tank in $15$ hours and $20$ hours respectively,while a third pipe $C$ can empty the full tank in $25$ hours. All three pipes are opened in the beginning. After $10$ hours,pipe $C$ is closed. Find the total time (in hours) in which the tank will be full.

Three pipes $A, B$ and $C$ can fill a tank in $6$ $hours$. After running them together for $2$ $hours$, the tap $C$ is closed and $A$ and $B$ fill the remaining part in $7$ $hours$. How much time (in $hours$) would $C$ take to fill the tank alone?

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