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?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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