A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed, then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open, then the inlet- pipe fills the empty tank in 10 hours. If only the outlet pipe is open, then in how many hours the full tank becomes half-full?

Given:

Inlet pipe fills the empty tank in 8 hours.

Inlet pipe fills the empty tank in 10 hours with the outlet pipe open.

Formula Used:

Rate of work = Work / Time

Combined rate of inlet and outlet pipes = Inlet rate - Outlet rate

Calculation:

Let the tank capacity be 1 unit.

Inlet pipe rate = 1 / 8 units/hr

Combined rate when both pipes are open = 1 / 10 units/hr

Let Outlet pipe rate = x units/hr

Combined rate = Inlet rate - Outlet rate

⇒ 1 / 10 = 1 / 8 - x

⇒ x = 1 / 8 - 1 / 10

⇒ x = (10 - 8) / (8 × 10)

⇒ x = 2 / 80

⇒ x = 1 / 40 units/hr

The outlet pipe empties the tank at a rate of 1 / 40 units/hr.

To find the time for the full tank to become half-full:

Rate of emptying = 1 / 40 units/hr

Time to empty half the tank (0.5 units):

Time = Work / Rate

Time = 0.5 / (1 / 40)

Time = 0.5 × 40

Time = 20 hrs

The full tank becomes half-full in 20 hours.