A water tank has a leak at its bottom which can completely drain the full tank in 8 hours. There is also an inlet pipe that adds water at a rate of 6 liters per minute. When the tank is initially full and both the leak and inlet pipe are functioning, the tank empties in 12 hours. What is the total capacity of the tank?

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Let's analyze the rates at which water enters and leaves the tank:

The leak empties a full tank in 8 hours, so the **rate of emptying** = 1/8 of the tank per hour.

The inlet pipe adds **6 liters per minute** = 6 × 60 = **360 liters per hour**.

When both the leak and inlet pipe are operating together, the tank empties in 12 hours. This means the **net emptying rate** is 1/12 of the tank per hour.

Now we can calculate the work done by the inlet pipe:
**Work done by the inlet** = Rate of emptying by leak - Net emptying rate
= 1/8 - 1/12
= 3/24 - 2/24
= 1/24 of the tank per hour

In other words, the inlet pipe fills **1/24** of the tank per hour.

Converting to minutes:
**Work done by inlet in 1 minute** = 1/24 × 1/60 = **1/1440** of the tank

Since the inlet adds 6 liters per minute, this means:
**1/1440 part of the tank** = 6 liters

Therefore:
**Total tank capacity** = 1440 × 6 = **8640 liters**

We can verify this answer:
- Leak empties at 8640/8 = 1080 liters per hour
- Inlet fills at 360 liters per hour
- Net emptying rate = 1080 - 360 = 720 liters per hour
- Time to empty = 8640/720 = 12 hours ✓

Therefore, the tank holds **8640 liters** of water.

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