Pipes and Cistern


  1. Pipe A can fill a Tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?









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    Part filled by A in 1 min = 1/30
    Part filled by B in 1 min = 1/10
    Part emptied by C in 1 min = - 1/40
    Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )

    Correct Option: A

    Part filled by A in 1 min = 1/30
    Part filled by B in 1 min = 1/10
    Part emptied by C in 1 min = - 1/40
    Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )
    = (4 + 12 - 3)/120 = 13/120

    ∴ Required time to fill the tank = 120/13 = 93/13 h


  1. Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?









  1. View Hint View Answer Discuss in Forum

    Let the leak takes x h to empty the tank.
    Now, part filled by inlet in 1 h = 1/8
    part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10

    According to the question.
    1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40

    Correct Option: D

    Let the leak takes x h to empty the tank.
    Now, part filled by inlet in 1 h = 1/8
    part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10

    According to the question.
    1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40
    ∴ x = 40 h



  1. Two pipes A and B can fill a tank in 1 h and 75 min, respectively. There is also an outlet C . If all the three pipes are opened together. The tank is full 50 min. How much time will be taken by C to empty the full tank?









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    Work done by C in 1 min = (1/60 + 1/75 - 1/50 )
    = (5 + 4 - 6)/300 = 3/300 = 1/100

    Correct Option: A

    Work done by C in 1 min = (1/60 + 1/75 - 1/50 )
    = (5 + 4 - 6)/300 = 3/300 = 1/100
    Hence, C can empty the full tank in 100 min.


  1. A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. in how much time A, B and C fill up the tank together?









  1. View Hint View Answer Discuss in Forum

    Part filled by ( A + B ) in 1 h = 1/6
    Part filled by ( B + C ) in 1 h = 1/10
    Part filled by ( A + C ) in 1 h = 1/12
    ∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
    ∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40

    Correct Option: D

    Part filled by ( A + B ) in 1 h = 1/6
    Part filled by ( B + C ) in 1 h = 1/10
    Part filled by ( A + C ) in 1 h = 1/12
    ∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
    ∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40
    ∴ Required time 40/7 = 55/7 h



  1. Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?









  1. View Hint View Answer Discuss in Forum

    Part filled by pipe P in 1 min = 1/12
    Part filled by pipe Q in 1 min = 1/15
    Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
    Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
    ∴ Remaining part = 1 - 9/20 = 11/20

    Correct Option: A

    Part filled by pipe P in 1 min = 1/12
    Part filled by pipe Q in 1 min = 1/15
    Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
    Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
    ∴ Remaining part = 1 - 9/20 = 11/20
    Let the remaining part is filled by pipe Q in T min.
    Then, T/15 = 11/20
    T = (15 x 11)/20 = (3 x 11)/4
    = 33/4 = 84/4 min