Pipe P can fill a tank in 12 hours, while pipe Q can fill the same tank in 20 hours. Both pipes are initially opened to fill an empty tank, but after 5 hours, pipe Q is closed. To figure out how much less time would have been required to fill the tank if pipe Q had not been closed, considering the dynamic flow rates of both pipes, you need to determine the alternative completion time.
We can say that Let the total capacity of the tank = 60 units (L.C.M of 12 & 20) Efficiency of P = 60/12 = 5 units/hr Efficiency of Q = 60/20 = 3 units/hr Time taken to fill the tank when both the pipes work together = 60/(5 + 3) = 7.5 hours According to the question, Tank filled in 5 hours = (5 + 3) × 8 = 40 units Remaining capacity of tank = 60 – 40 = 20 units Time taken by Pipe P to fill the remaining part = 20/5 = 4 hours Total time taken = 5 + 4 = 9 hours Extra time taken = 9 – 7.5 = 1.5 hrs
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