Leak vs. compensating inflow (capacity from times) A tank has a leak that would empty it in 8 hours. A tap admitting 3 L per minute is turned on, and now the tank empties in 12 hours. What is the capacity of the tank?

Introduction / Context:
This is a capacity-from-rate-difference problem. Treat the leak as a constant outflow and the tap as a constant inflow. The observed emptying time under compensation identifies the net outflow; solving two linear relations yields the tank volume.

Given Data / Assumptions:

• Leak alone empties in 8 h ⇒ leak rate = V/8 per hour = V/480 per min.
• With 3 L/min added, emptying time is 12 h ⇒ net outflow = V/12 per hour = V/720 per min.
• V = tank capacity in liters.

Concept / Approach:
Net outflow (leak − 3) equals V/720. Set up the equation using leak-alone rate and solve for V.

Step-by-Step Solution:

Verification / Alternative check:
Check: leak 540 L/h; tap 180 L/h in; net 360 L/h ⇒ 4320/360 = 12 h.

Why Other Options Are Wrong:
4000, 2250, 4120 do not satisfy both time conditions simultaneously.

Common Pitfalls:
Mistaking hours for minutes or mixing units inside the same equation.

Final Answer:
4320 L