Question

    Three pipes P, Q and R can fill a cistern in 40 minutes,

    80 minutes and 120 minutes, respectively. Initially, all the pipes are opened. After how much time (in minutes) should the pipes Q and R be turned off so that the cistern will be completely filled in just half an hour?
    A 14 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 16 Correct Answer Incorrect Answer
    D 12 Correct Answer Incorrect Answer

    Solution

    Assume total work = 240 units (LCM of 40, 80, 120).
    Efficiencies: P = 6 units/min, Q = 3 units/min, R = 2 units/min. Let Q and R be turned off after x minutes. Work in first x minutes = (6 + 3 + 2 ) × x = 11x Work in remaining 30 − x minutes by P =  6(30 − x) 11 x  +  6 ( 30  −  x )  =  240  ⇒ 11 x  +  180  −  6 x  =  240  ⇒ 5 x  =  60  ⇒ x  =  12

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