A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is plugged. If there is a leakage also which is capable of draining out the liquid from the tank at half of the rate of outlet pipe,them what is the time taken to fill the empty tank when both the pipes are opened?
A. 3 hours
B. 4 hours
C. 5 hours
D. None of these
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Work rate of inlet pipe = 100/2 = 50% per hour.
Negative Work rate of outlet pipe = 100/6 = 16.66% per hour.
Negative work rate of leakage = 16.66/2 = 8.33%.
Time taken to fill the empty tank = 100/(50 - 16.66 - 8.33) = 100/25 = 4 hours.