Question
A tank can be filled by pipe A in 10 hours and by pipe B
in 15 hours. Pipe C can empty the full tank in 12 hours. All three pipes are opened together. After some time, pipe C is closed and the tank gets completely filled in a total of 8 hours. For how many hours was pipe C open?Solution
Assume tank capacity = 60 units. Rates: A fills in 10 h ⇒ 6 units/h B fills in 15 h ⇒ 4 units/h C empties in 12 h ⇒ −5 units/h. When all three are open: Net rate = 6 + 4 − 5 = 5 units/h. When only A and B are open: Net rate = 6 + 4 = 10 units/h. Let C be open for t hours (with A and B), and then closed for (8 − t) hours. Work done: (When all three open) 5t (When only A & B open) 10(8 − t). Total work = 60: 5t + 10(8 − t) = 60 5t + 80 − 10t = 60 80 − 5t = 60 5t = 20 t = 4. Answer: Pipe C was open for 4 hours.
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