(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

$A$ pipe $P$ can fill a tank in $12$ $min$ and another pipe $R$ can fill it in $15$ $min.$ But,the $3$rd pipe $M$ can empty it in $6$ $min.$ The $1$st two pipes $P$ and $R$ are kept open for $5$ $min$ in the beginning and then the $3$rd pipe is also opened. In what time (in minutes) is the tank emptied?

Medium

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There are two taps $A$ and $B$ to fill up a water tank. The tank can be filled in $40$ $min,$ if both taps are on. The same tank can be filled in $60$ $min,$ if tap $A$ alone is on. How much time (in $minutes$) will tap $B$ alone take to fill up the same tank?

Easy

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Two pipes $A$ and $B$ can fill a tank in $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

Easy

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Three pipes $A, B$ and $C$ can fill a cistern in $6$ $hrs$. After working together for $2$ $hrs$,$C$ is closed and $A$ and $B$ fill the remaining part of the cistern in $8$ $hrs$. Find the time (in $hrs$) in which the cistern can be filled by pipe $C$ alone.

Medium

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$A$ tap can fill a cistern in $40$ $min$ and a second tap can empty the filled cistern in $60$ $min$. By mistake, without closing the second tap, the first tap was opened. In how many $minutes$ will the empty cistern be filled?

Medium

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There are two taps $A$ and $B$ to fill up a water tank. The tank can be filled in $40$ $min,$ if both taps are on. The same tank can be filled in $60$ $min,$ if tap $A$ alone is on. How much time (in $minutes$) will tap $B$ alone take to fill up the same tank?

Two pipes $A$ and $B$ can fill a tank in $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

Three pipes $A, B$ and $C$ can fill a cistern in $6$ $hrs$. After working together for $2$ $hrs$,$C$ is closed and $A$ and $B$ fill the remaining part of the cistern in $8$ $hrs$. Find the time (in $hrs$) in which the cistern can be filled by pipe $C$ alone.

$A$ tap can fill a cistern in $40$ $min$ and a second tap can empty the filled cistern in $60$ $min$. By mistake, without closing the second tap, the first tap was opened. In how many $minutes$ will the empty cistern be filled?

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