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Discussion :: Pipes and Cistern

  1. Two pipes A and B can fill a cistern in 3 \( \frac { 1 } { 2 } \) minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

    2. A.

    5 min.
    B.

    9 min.
    C.

    10 min.
    D.

    15 min.

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    Answer : Option B

    Explanation :

    Let B be turned off after x minutes. Then,

     

    Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

     

     x [\(\frac { 2 } { 75 } \)+ \(\frac { 1 } { 45 } \)] + (30-x) \(\frac { 2 } { 75 } \)=1 

     

    \(\frac { 11X } { 225 } \)+ \( \frac {(60-2X0 } { 75 } \) =1

     

     11x + 180 - 6x = 225.

     

     x = 9.

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