Nitin installed an overhead tank on the roof of his newly constructed house. Three taps are connected to the tank: 2 taps A and B to fill the tank and one tap C to empty it. Tap A alone can fill the tank in 12 hours, while tap B alone takes one and a half times more time than tap A to fill the tank completely. Tap C alone can empty a completely filled tank in 36 hours. Yesterday, to fill the tank, Nitin first opened tap A, and then after 2 hours opened tap B also. However after 6 hours he realised that tap C was open from the very beginning. He quickly closes tap C. What will be the total time required to fill the tank?
Explanation:
Tab B takes 1.5 times more than tap A to fill the tank.
A takes 12 hours to fill the tank alone.
Hence, time taken by tap B alone = 1.5 × 12 = 18 hours
Let the total capacity of the tank be 180 litres.
Let taps A and B fill a and b litres per hour and let tap C empty c litres per hour.
∴ a = 180/12 = 15; b = 180/18 = 10 and c = 180/36 = 5
For the first two hours, only A and C are working; for the next four hours, all three of A, B and C are working and for the next n hours, only A and B are working.
∴ 2(a – c) + 4(a + b – c) + n(a + b) = 180
∴ 2(15 – 5) + 4(15 + 10 – 5) + n(15 + 10) = 180
∴ 2(10) + 4(20) + 25n = 180
∴ 25n = 180 – 20 – 80 = 80
∴ n = 80/25 = 3.2 hours
∴ Total time = 6 + 3.2 = 9.2 hours
i.e. 9 hours and 12 minutes
Hence, option (c).
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