Directions : Answer the question independently. Water is being poured into a tank at a constant rate using an inlet pipe. There are a number of outlet pipes of equal capacities attached to the tank. Initially the tank is full and all the inlet and outlet pipes are open. It is observed 10 outlet pipes empty the tank in 12 hrs, while 15 pipes empty the tank in 6 hrs. In how much time (in hours) would 25 pipes empty the tank, if the tank is initially full?

Let the inlet pipe fill at I units per hour, one outlet pipe empty at O units per hour, and the total capacity be C. For 10 outlet pipes, the net rate is 10O - I = C/12, and for 15 pipes, the net rate is 15O - I = C/6. Subtracting the first equation from the second gives 5O = C/12, which simplifies to C = 60O. Substituting this back into the first equation yields the inlet rate I = 5O. For 25 outlet pipes, the net emptying rate is 25O - 5O = 20O. Since the total capacity is 60O, the time to empty the tank is 60O / 20O, which is 3 hours.

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