Pipes and Cistern


  1. A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak ?









  1. View Hint View Answer Discuss in Forum

    From the given question ,

    ∴ Part of the cistern filled by pipe in 1 hour =
    1
    9

    Due to a leakage ,Part of the cistern filled by pipe in 1 hour =
    1
    10

    Part of the tank emptied by the leak in 1 hour =
    1
    -
    1
    910

    Correct Option: C

    From the given question ,

    ∴ Part of the cistern filled by pipe in 1 hour =
    1
    9

    Due to a leakage ,Part of the cistern filled by pipe in 1 hour =
    1
    10

    Part of the tank emptied by the leak in 1 hour =
    1
    -
    1
    910

    Part of the tank emptied by the leak in 1 hour =
    10 - 9
    =
    1
    9090

    ∴ Required time = 90 hours


  1. Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time (in hours) in which the tank can be filled by pipe C alone is









  1. View Hint View Answer Discuss in Forum

    On the basis of given details in question ,

    ∴ Part of the tank filled by (A + B + C) in 1 hour =
    1
    6

    Part of tank filled by these in 2 hours =
    2
    =
    1
    63

    Remaining part = 1 -
    1
    =
    2
    33

    Time taken by A and B in filling
    2
     rd part = 8 hours
    3

    ∴ Time taken by A and B in filling the whole tank =
    8 × 3
    = 12 hours
    2

    Correct Option: B

    On the basis of given details in question ,

    ∴ Part of the tank filled by (A + B + C) in 1 hour =
    1
    6

    Part of tank filled by these in 2 hours =
    2
    =
    1
    63

    Remaining part = 1 -
    1
    =
    2
    33

    Time taken by A and B in filling
    2
     rd part = 8 hours
    3

    ∴ Time taken by A and B in filling the whole tank =
    8 × 3
    = 12 hours
    2

    ∴ Part of tank filled by C in an hour =
    1
    -
    1
    =
    1
    61212

    Hence, required time = 12 hours



  1. Two pipes A and B can fill a tank in 6 hours and 8 hours respectively. If both the pipes are opened together, then after how many hours should B be closed so that the tank is full in 4 hours?









  1. View Hint View Answer Discuss in Forum

    As per the given in question , we have

    Part of the tank filled in 4 hours by pipe A =
    4
    =
    2
    63

    Remaining part = 1 -
    2
    =
    1
    33

    Time taken by pipe B in filling
    1
     part =
    8
      hours
    33

    We can find required answer with the help of given formula :
    Here, p = 6,q = 8, t = 4
    Required time = q 1 -
    t
    p

    Correct Option: D

    As per the given in question , we have

    Part of the tank filled in 4 hours by pipe A =
    4
    =
    2
    63

    Remaining part = 1 -
    2
    =
    1
    33

    Time taken by pipe B in filling
    1
     part =
    8
      hours
    33

    We can find required answer with the help of given formula :
    Here, p = 6,q = 8, t = 4
    Required time = q 1 -
    t
    p

    Required time = 8 1 -
    4
    6

    Required time =
    8
    hours
    3


  1. Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened simultaneously, but after two hours, pipe A is closed. How many hours will B take to fill the remaining part of the cistern ?









  1. View Hint View Answer Discuss in Forum

    On the basis of given details in question ,

    Part of the cistern filled in 2 hours by pipe A and B = 2
    1
    +
    1
    = 2
    4 + 3
    =
    7
    682412

    Remaining part = 1 -
    7
    =
    5
    1212

    Correct Option: B

    On the basis of given details in question ,

    Part of the cistern filled in 2 hours by pipe A and B = 2
    1
    +
    1
    = 2
    4 + 3
    =
    7
    682412

    Remaining part = 1 -
    7
    =
    5
    1212

    ∴ Time taken by pipe B in filling 5/12 part =
    5
    × 8 =
    10
    = 3
    1
    hours.
    1233



  1. A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in :









  1. View Hint View Answer Discuss in Forum

    According to question , we have

    Part emptied by the leak in 1 hour =
    1
    -
    1
    =
    5 - 4
    =
    1
    8104040

    Correct Option: D

    According to question , we have

    Part emptied by the leak in 1 hour =
    1
    -
    1
    =
    5 - 4
    =
    1
    8104040

    ∴ The leak will empty the cistern in 40 hours.