Question

# Pipe A takes 34 of the times required by pipe B to fill the empty tank individually. When an outlet pipe C is also opened simultaneously with pipe A and pipe B, it takes34 more time to fill the empty tank than it takes, when only pipe A and pipe B are opened together, If it takes to fill 33 hours when all the three pipes are opened simultaneously, then in what time pipe C can empty the full tank operating alone?

A
66 hours
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B
50 hours
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C
44 hours
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D
can't be determined
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Solution

## The correct option is B 44 hoursLet pipe A fill the tank in 3x hours then pipe B fill it in 4x hours. Therefore, in 1 hour they will fill = 13x+14x=712x i.e., they will take 12x7 hours When an outlet pipe C is also opened then it takes =12x7+12x7×34=12x7(74)=3x hours Now, in one hour pipe A, B and C working together fill =13x+14x−1C=13x⇒ 112x−1C=13x⇒ 1C=(112x−13x)⇒ C=4x Hence, in 4x hours pipe C can empty the whole tank. Now, since 3x=33⇒x=11 ∴ 4x=4×11=44 hours

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