Question
Pipe A can fill a tank in 24 minutes, Pipe B can fill it
in 36 minutes and Pipe C can empty it in 48 minutes. All three pipes are opened together, but Pipe C is closed after some time. The tank gets filled completely in 18 minutes.ย For how many minutes was Pipe C open?Solution
ATQ, A's 1-minute work = 1/24 B's 1-minute work = 1/36 C's 1-minute work = -1/48 So, work done per minute by all three together = 1/24 + 1/36 - 1/48 = 6/144 + 4/144 - 3/144 = 7/144 Let Pipe C remain open for x minutes. Work done in x minutes = 7x/144 For remaining (18 - x) minutes, only A and B work. A + B per minute work = 1/24 + 1/36 = 6/144 + 4/144 = 10/144 Work done in remaining time = (18 - x) ร 10/144 Total work = 1 So, 7x/144 + 10(18 - x)/144 = 1 7x + 180 - 10x = 144 -3x = -36 x = 12 Hence, Pipe C was open for 12 minutes.
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