Question
Three pipes A, B and C can fill/empty a tank. A can fill it in 12 hours, B in 15 hours, and C can empty a full tank in 20 hours. All three pipes are opened together. After some time, pipe C is closed and A and B together fill the remaining tank in 5 hours. If the tank is exactly full at the end, for how many hours was pipe C kept open?
Solution
ATQ, Filling rates: A = 1/12, B = 1/15, C (emptying) = −1/20 (per hour). A + B = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20. A + B + C = 3/20 − 1/20 = 2/20 = 1/10. Let C be open for x hours (all three working). Volume filled in this time = x × (1/10) = x/10. After C is closed, A + B work for 5 hours: Volume filled = 5 × (3/20) = 15/20 = 3/4. Total volume = 1 ⇒ x/10 + 3/4 = 1 ⇒ x/10 = 1 − 3/4 = 1/4 ⇒ x = 2.5 hours.
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