Inlet with leakage (net fill) A tap can fill an empty tank in 12 hours, and a leakage can empty the full tank in 20 hours. If both act together, how long will the tank take to become full?

Introduction / Context:
A leak is like an outlet with a constant negative rate. With one inlet and one leak, the net rate is inlet minus leak. The fill time is the reciprocal of the net rate.

Given Data / Assumptions:

• Inlet time = 12 h ⇒ rate = 1/12.
• Leak time (emptying) = 20 h ⇒ rate = 1/20 (negative).
• Rates are constant; tank volume is 1 unit.

Concept / Approach:
Net rate = 1/12 − 1/20. Use common denominator to subtract, then invert.

Step-by-Step Solution:

Verification / Alternative check:
In 30 h, the inlet adds 30/12 = 2.5 tanks; the leak removes 30/20 = 1.5 tanks; net = 1 tank.

Why Other Options Are Wrong:
25, 35, 40 produce incorrect net balances when checked.

Common Pitfalls:
Adding times instead of subtracting rates, or miscomputing the common denominator.

Final Answer:
30 h