Pipes and Cistern


  1. A cistern can be filled with water by a pipe in 5 hours and it can be emptied by a second pipe in 4 hours. If both the pipes are opened when the cistern is full, the time in which it will be emptied is :









  1. View Hint View Answer Discuss in Forum

    According to the question ,

    Cistern filled in 1 hour =
    1
    part
    5

    Cistern emptied in 1 hour =
    1
    part
    4

    When the both pipes are opened, simultaneously ;
    Cistern emptied in 1 hour =
    1
    -
    1
    =
    5 - 4
    =
    1
    part
    452020

    ∴ The time in which it will be emptied = 20 hours.
    Using the given formula :
    Here, p = 5, q = 4
    Required time =
    pq
    hrs
    (p - q)

    Correct Option: C

    According to the question ,

    Cistern filled in 1 hour =
    1
    part
    5

    Cistern emptied in 1 hour =
    1
    part
    4

    When the both pipes are opened, simultaneously ;
    Cistern emptied in 1 hour =
    1
    -
    1
    =
    5 - 4
    =
    1
    part
    452020

    ∴ The time in which it will be emptied = 20 hours.
    Using the given formula :
    Here, p = 5, q = 4
    Required time =
    pq
    hrs
    (p - q)

    Required time =
    5 × 4
    = 20 hrs.
    5 - 4


  1. A tap can empty a tank in one hour. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?









  1. View Hint View Answer Discuss in Forum

    We know that , 1 hour = 60 minutes.
    Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
    When both operate simultaneously ,

    Rate of emptying the tank =
    1
    +
    1
    =
    1 + 2
    =
    3
    =
    3
    of the tank per minute.
    6030606020

    ∴ Time taken by the two taps together to empty the tank = 20 minutes
    Second method to solve this question :
    Here, p = 60, q = 30
    Required time =
    pq
    minutes
    (p + q)

    Correct Option: A

    We know that , 1 hour = 60 minutes.
    Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
    When both operate simultaneously ,

    Rate of emptying the tank =
    1
    +
    1
    =
    1 + 2
    =
    3
    =
    3
    of the tank per minute.
    6030606020

    ∴ Time taken by the two taps together to empty the tank = 20 minutes
    Second method to solve this question :
    Here, p = 60, q = 30
    Required time =
    pq
    minutes
    (p + q)

    Required time =
    60 × 30
    minutes
    60 + 30

    Required time = 20 minutes.



  1. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is :









  1. View Hint View Answer Discuss in Forum

    As per the given in question , we have

    Part of the tank filled by both pipes in one minute =
    1
    +
    1
    2030

        1
    Required time =
    1
    +
    1
    2030

    Required time =
    20 × 30
    = 12 minutes
    50

    We can find required answer with the help of given formula :
    Here, p = 20, q = 30
    Required time =
    pq
    minutes.
    p + q

    Correct Option: B

    As per the given in question , we have

    Part of the tank filled by both pipes in one minute =
    1
    +
    1
    2030

        1
    Required time =
    1
    +
    1
    2030

    Required time =
    20 × 30
    = 12 minutes
    50

    We can find required answer with the help of given formula :
    Here, p = 20, q = 30
    Required time =
    pq
    minutes.
    p + q

    Required time =
    20 × 30
    minutes.
    20 + 30

    Required time = 12 minutes.