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The problem you provided is about a tank with a leak and a tap filling water. Let's solve this step-by-step.

### Problem Statement Recap:
- The tank empties in **6 hours** due to a leak.
- A tap is turned on, filling the tank with **10 liters of water per minute**.
- With the tap on, the tank now takes **10 hours** to empty.
- We need to find the capacity of the tank in liters.

### Step-by-Step Solution:

1. **Rate of emptying due to leak**:
   - Without the tap, the tank empties in 6 hours. Let the capacity of the tank be \( C \) liters.
   - The rate at which the tank is emptying due to the leak is \( \frac{C}{6} \) liters per hour.

2. **Water input from the tap**:
   - The tap fills the tank at a rate of **10 liters per minute**, which is:
     \[
     10 \times 60 = 600 \, \text{liters per hour}.
     \]
   
3. **Net rate when both tap and leak are working**:
   - With both the leak and the tap operating, the tank takes **10 hours** to empty.
   - The combined net rate of emptying is \( \frac{C}{10} \) liters per hour (since it takes 10 hours to empty).

4. **Setting up the equation**:
   - When the tap is on, the leak is still present, so the rate at which the tank is losing water is the difference between the leak rate and the tap’s filling rate:
     \[
     \text{Net rate} = \text{Leak rate} - \text{Tap rate}.
     \]
     Substituting values:
     \[
     \frac{C}{10} = \frac{C}{6} - 600.
     \]
   
5. **Solving the equation**:
   - First, solve for \( C \):
     \[
     \frac{C}{10} + 600 = \frac{C}{6}.
     \]
   - Multiply the entire equation by 30 to eliminate the denominators:
     \[
     3C + 18000 = 5C.
     \]
   - Rearrange the terms:
     \[
     18000 = 5C - 3C,
     \]
     \[
     18000 = 2C.
     \]
   - Finally, solve for \( C \):
     \[
     C = \frac{18000}{2} = 9000 \, \text{liters}.
     \]

### Conclusion:
The capacity of the tank is **9000 liters**.

Would you like more details, or do you have any questions?

### Related Questions:
1. What would happen if the tap filled at a different rate?
2. How long would the tank take to empty if the leak was larger?
3. How much water is lost due to the leak alone in 10 hours?
4. If the tank were twice as large, how would the leak and fill rates change?
5. How do you calculate the capacity of a tank if there were no leaks?

### Tip:
When solving word problems, always start by writing out what each part of the problem represents.

There is a leak in a tank which empties it in 6 hours. A tap is turned on which fills the tank with 10 liters of water per minute. When it is full, it now takes 10 hours to empty. What is the capacity (in liters) of the tank?

Learn how to solve a word problem involving a tank with a leak and a tap that fills water at a given rate. The tank empties in 6 hours, but with a tap filling it, it now takes 10 hours. This problem involves algebra and flow rate calculations, suitable for students in Grades 8-10.

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