A tank has an optional adjustable outlet pipe that can be attached to the tank at any height we want. This outlet pipe drains water from the tank at a constant rate, while the tank is being filled using another inlet pipe at a constant rate. If the outlet, pipe is attached at half the height of the tank, the tank, which is initially empty gets filled in 18 hours. If the outlet pipe is attached at height equal to two third height of the tank, the tank, which is initially empty, is filled in 16 hours. In how many hours will the tank, which is initially empty, be completely filled if the outlet pipe is not attached to the tank? Correct Answer 12 hours Suppose the time taken to fill the first half of the tank in the first situation = ‘a’ hours Time taken to fill the second half of the tank in the first situation = ‘b’ hours a + b = 18 hours ----(1) If the time taken by only the inlet pipe to fill half part of the tank is ‘a’ hours, then the time taken by the inlet pipe to fill the (2/3)rd part of the tank = (4/3)a hours If the time taken by the inlet and outlet pipes together to fill half part of the tank is ‘b’ hours, then the time taken by both of them to fill the remaining (1/3)rd part of the tank in the second scenario = (2/3)b hours (4/3)a + (2/3)b = 16 ----(2) Solving equation 1 and 2, we get a = 6, b = 12 Time taken by the inlet pipe to fill half the tank = 6 hours ∴ Time taken by the inlet pipe to fill full tank = 12 hours