Question
A, B and C are three pipes connected to a tank. A and B
together fill the tank in 15 hrs. B and C together fill the tank in 20 hrs. A and C together fill the tank in 30 hrs. In how much time will B alone fill the tank?Solution
A + B fill in 15 hrs B + C fill in 20 hrs A + C fill in 30 hrs ⇒ 2 (A + B+ C) fill in (15 × 20 × 30)/(30 × 20 + 15 × 30 + 15 ×20) = 20/3 hours ∴ A + B + C fill the tank in 40/3 hours Now, C = (A + B+ C) – (B + C) ] fills in 3/40 - 1/15 = 1/120 or 120 hours Similarly, A fills in 3/40 - 1/20 = 1/40 or 40 hours And B fills in 3/40 - 1/30 = 1/24 or 24 hours
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