An inlet pipe can fill an empty tank in hours while an outlet pipe drains a completely filled tank in hours. The tank is initially empty, and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 20.
The inlet pipe fills the tank = hours
The outlet pipe drains the tank = hours
Let's assume the capacity of the tank = LCM of (and ) = 36 unit
Efficiency of Inlet pipe = 36/(9/2) = 8 unit/h
Efficiency of outlet pipe = 36/(36/5) = -5 unit/h
They can fill the tank = 2 hours = 8 - 5 = 3 unit
20 hours = 30 unit
Remaining capacity = 36 - 30 = 6 units, which is filled by the inlet pipe
= 6/8 = 3/4 hours
Total time = 20 + 3/4 = 20 hours