Pipes and Cistern

Pipes and Cistern

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  1. Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes, 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack take to empty it ?








  1. View Hint View Answer Discuss in Forum

    Let the leak empties it in T hours
    From the given rule, we have (T x 30) / (T - 30) = 40

    Correct Option: B

    Let the leak empties it in T hours
    From the given rule, we have (T x 30) / (T - 30) = 40
    ∴ T = 120 minutes = 2 hours.

    Now, from the question, applying the rule, we have time taken by B to fill the tank when crack in the bottom develops
    = (120 x 40) / (120 - 40) = 60 minutes = 1 hour

  1. A cistern can be filled by one of two pipes in 30 minutes and by the other in 36 minutes. Both pipes are opened together for a certain time but being particularly clogged only 5 / 6 of the full quantity of water flows through the former and only 9 / 10 through the later. The obstructions, however, being suddenly removed the cistern is filled in 151/2 minutes from that moment. How long was it before the full flow of water began ?








  1. View Hint View Answer Discuss in Forum

    Net filling in last 151/2 minutes
    = 31/2 (1/30 + 1/36) = 341/360
    Now, suppose they remained clogged for x minutes.
    Net filling in these x minutes
    = (x/30 x 5/6 + x/36 x 9/10) = 19 x/360

    Correct Option: A

    Net filling in last 151/2 minutes
    = 31/2 (1/30 + 1/36) = 341/360
    Now, suppose they remained clogged for x minutes.
    Net filling in these x minutes
    = (x/30 x 5/6 + x/36 x 9/10) = 19 x/360
    Remaining part = (1 - 19x/360) = (360 - 19x/360)
    360 - 19x/360 = 341/360 or x = 1.
    Hence, the pipes remained clogged for 1 minutes.

  1. Three taps A,B and C can fill a cistern in 10, 15 and 20 minutes respectively. They are all turned on at once, but after 3 minutes C is turned off. How many minutes longer will A and B take to fill the cistern ?








  1. View Hint View Answer Discuss in Forum

    T = (10 x 15 x 20) / (10 x 15 + 10 x 20 + 15 x 20) = 60/13 minutes

    Correct Option: B

    T = (10 x 15 x 20) / (10 x 15 + 10 x 20 + 15 x 20) = 60/13 minutes
    Now, applying the given rule, we have [60/13 x y]/ [y - 60/13 + 3] = 20
    or y = 21/10 = 2 min. 6 seconds.