Pipes and Cistern

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  1. Two taps A and B can fill a tank in 25 min and 20 min, respectively. But taps are not opened properly so the taps A and B allow 5/6th and 2/3rd part of water, respectively. How long will they take to fill the tank?








  1. View Hint View Answer Discuss in Forum

    Part of the tank filled with A and B in
    1 min = 1/25 x 5/6 + 1/20 x 2/3 = 1/30 + 1/30
    = 2/30 = 1/15

    Correct Option: A

    Part of the tank filled with A and B in
    1 min = 1/25 x 5/6 + 1/20 x 2/3 = 1/30 + 1/30
    = 2/30 = 1/15
    Hence, Time taken to fill the tank = 15 min

  1. Two taps A and B can fill a tank in 20 min and 30 min, respectively. An outlet pipe C can empty the full tank in 15 min. A, B and C are opened alternatively, each for 1 min. How long will the tank take to be filled?








  1. View Hint View Answer Discuss in Forum

    Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
    ∴ Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
    Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
    Tap A fill 1/0 part in 1 min, then
    Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
    i.e, 1/30th part is filled by B in 1 min
    Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min

    Correct Option: C

    Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
    ∴ Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
    Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
    Tap A fill 1/0 part in 1 min, then
    Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
    i.e, 1/30th part is filled by B in 1 min
    Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min

  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