Pipes and Cistern


  1. A tank has a leak which would empty it in 8 h. A tap is turned on which admits 3 L a min into the tank and it is now emptied in 12 h. How many litres does the tank hold?









  1. View Hint View Answer Discuss in Forum

    Work done by the inlet in 1 h = (1/8 - 1/24) = 1/24
    Work done by the inlet in 1 min = 1/24 x 1/60 = 1/1440
    ∴ Volume of 1/1440 part = 3 L

    Correct Option: A

    Work done by the inlet in 1 h = (1/8 - 1/24) = 1/24
    Work done by the inlet in 1 min = 1/24 x 1/60 = 1/1440
    ∴ Volume of 1/1440 part = 3 L
    ∴ Volume of the whole = 3 x 1440 = 4320 L


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









  1. View Hint View Answer Discuss in Forum

    Time taken by A to fill the tank, m = 15 min
    ∴ Time taken by B to fill the tank, n = 15 x 4 = 60
    ∴ Required time taken m x n/(m + n)

    Correct Option: B

    Time taken by A to fill the tank, m = 15 min
    ∴ Time taken by B to fill the tank, n = 15 x 4 = 60
    ∴ Required time taken m x n/(m + n)
    = (15 x 60)/(15 + 60) = (15 x 60)/75 = 12 min



  1. There are two inlets A and B connected to a tank. A and B can fill the tank in 16 h and 10 h, respectively. If both the pipes are opened alternately for 1 h, starting from A, then how much time will the tank take to filled?









  1. View Hint View Answer Discuss in Forum

    Part filled by A in 1 h = 1/16
    Part fill by B in 1 h = 1/10
    Part filled by ( A + B ) in 2 h = 1/16 + 1/10 = 13/80
    ∴ Part filled by ( A + B ) in 12 h = 6 x 13/80 = 78/80
    ∴ Remaining part = 1 - 78/80 = 2/80 = 1/40

    Correct Option: C

    Part filled by A in 1 h = 1/16
    Part fill by B in 1 h = 1/10
    Part filled by ( A + B ) in 2 h = 1/16 + 1/10 = 13/80
    ∴ Part filled by ( A + B ) in 12 h = 6 x 13/80 = 78/80
    ∴ Remaining part = 1 - 78/80 = 2/80 = 1/40
    Now, it is the turn of A
    Time taken by A to fill 1/40 part of the tank = (1/40) x 16 = 2/5 h
    ∴ Total time taken ( 12 + 2/5) h = 122/5 h


  1. Two pipes X and Y can fill a cistern in 6 and 7 min, respectively. Starting with pipe X, both the pipes are opened alternately, each for 1 min. In what time will they fill the cistern?









  1. View Hint View Answer Discuss in Forum

    Part filled by X in 1st min and Y in the 2nd min = ( 1/6 + 1/7) = 13/42
    Part filled by ( X + Y ) working alternately in 6 min = 1/2 x 13/42 x 6 =13/14
    ∴ Remaining Part = ( 1- 13/14 ) = 1/14

    Correct Option: B

    Part filled by X in 1st min and Y in the 2nd min = ( 1/6 + 1/7) = 13/42
    Part filled by ( X + Y ) working alternately in 6 min = 1/2 x 13/42 x 6 =13/14
    ∴ Remaining Part = ( 1- 13/14 ) = 1/14
    Now, it is the turn of X, one-sixth part is filled in 1 min.
    One-fourteenth part is filled in (6 x 1/14) min = 3/7
    ∴ Required time = ( 6 + 3/7 ) = 63/7 min



  1. A tap having diameter 'd' empty a tank in 40 min. How long another tap having diameter '2d' take to empty the same tank?









  1. View Hint View Answer Discuss in Forum

    Area of tap ∝ Work done by pipe.
    When diameter is doubled, area will be four times. so, it will work four times faster.

    Correct Option: B

    Area of tap ∝ Work done by pipe.
    When diameter is doubled, area will be four times. so, it will work four times faster.
    Hence, required time taken to empty the tank = 40 x 1/4 = 10 min.