Question
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _________.
Options :
16.50
14.50
15.50
13.50
Answer :
14.50
Solution :
1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(1 /6 −1 /12) = 1/ 3
Tank filled by when Q and R works for another 6 hours = 6(1/ 9 −1 /12 = 1 /6
Total tank filled in these 10 hours = 1 /3 + 1/ 6 = 0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours
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