(C) Let the time taken by $A$ alone to fill the cistern be $x$ hours.Then,the time taken by $B$ alone to fill the cistern is $(x+6)$ hours.According t

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(C) Let the time taken by $A$ alone to fill the cistern be $x$ hours.Then,the time taken by $B$ alone to fill the cistern is $(x+6)$ hours.According to the problem,the combined rate of filling is $\frac{1}{x} + \frac{1}{x+6} = \frac{1}{4}$.Multiplying by $4x(x+6)$,we get $4(x+6) + 4x = x(x+6)$.$4x + 24 + 4x = x^2 + 6x$.$8x + 24 = x^2 + 6x$.$x^2 - 2x - 24 = 0$.Factoring the quadratic equation: $(x-6)(x+4) = 0$.Since time cannot be negative,$x = 6$.Therefore,pipe $A$ takes $6$ hours to fill the cistern alone.

Competitive Quantitative Aptitude Pipes and Cistern Pipes and Cistern

Difficult

Two pipes $A$ and $B$ together can fill a cistern in $4$ $hours$. Had they been opened separately,then $B$ would have taken $6$ $hours$ more than $A$ to fill the cistern. How much time (in $hours$) will be taken by $A$ to fill the cistern separately?

A
$1$
B
$2$
C
$6$
D
$8$

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Pipes and Cistern

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Pipes and Cistern

$A$ cistern is filled by two taps $A$ and $B$. Tap $A$ can fill it in $20$ $minutes$ and tap $B$ in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second tap $(B)$ is turned off. The cistern will be completely filled in another:

Medium

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Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)

Easy

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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?

Difficult

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Pipe $X$ can fill a tank in $20$ $hours$ and pipe $Y$ can fill the tank in $35$ $hours.$ Both the pipes are opened on alternate hours. Pipe $Y$ is opened first,then in how much time (in hours) will the tank be full?

Medium

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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?

Medium

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Two pipes $A$ and $B$ together can fill a cistern in $4$ $hours$. Had they been opened separately,then $B$ would have taken $6$ $hours$ more than $A$ to fill the cistern. How much time (in $hours$) will be taken by $A$ to fill the cistern separately?

Similar Questions

$A$ cistern is filled by two taps $A$ and $B$. Tap $A$ can fill it in $20$ $minutes$ and tap $B$ in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second tap $(B)$ is turned off. The cistern will be completely filled in another:

Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)

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?

Pipe $X$ can fill a tank in $20$ $hours$ and pipe $Y$ can fill the tank in $35$ $hours.$ Both the pipes are opened on alternate hours. Pipe $Y$ is opened first,then in how much time (in hours) will the tank be full?

$A$ 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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