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The problem involves repeatedly removing 2 liters of a 10-liter solution of milk and water and replacing it with pure milk. Let’s break this down step by step.

### Initial setup:
- Initial amount of milk: 8 liters in a 10-liter solution.
- After removing 2 liters, we replace it with pure milk.

### Formula:
At each step, \( \frac{2}{10} = \frac{1}{5} \) of the milk is removed. Hence, \( \frac{4}{5} \) of the milk remains. This is repeated three times.

The formula for the amount of milk after \( n \) repetitions is:
\[
M_n = M_0 \times \left(\frac{4}{5}\right)^n + (10 \times \left(1 - \left(\frac{4}{5}\right)^n\right))
\]
Where \( M_0 = 8 \) liters (initial milk content).

We will calculate the amount of milk after 3 replacements. Let me perform the calculation.After three repetitions of the process, the amount of milk in the mixture is approximately **8.976 liters**.

Therefore, the correct option is:

**Option 1: 8.976**

Would you like further details or have any questions? Here are some related questions you might explore:

1. How would the final amount of milk change if the solution initially had 7 liters of milk instead of 8?
2. What if the process was repeated four times instead of three?
3. How does increasing the volume of solution removed (e.g., 3 liters instead of 2 liters) affect the outcome?
4. What is the mathematical explanation for why milk approaches a certain limit as the process repeats?
5. How would the answer change if the initial solution contained a different total volume, such as 15 liters?

**Tip:** Repeated dilution problems often involve exponential decay, where each step reduces the remaining amount by a fixed fraction.

A 10-litre solution of milk and water contains 8 litres of milk. 2 litres of the solution is replaced by pure milk and mixed. The process is repeated two more times. How much milk (in litres) is present in the mixture so obtained?

Explore how repeated replacement in a milk-water mixture affects the milk concentration, using exponential decay and recurrent sequences. This problem is suitable for high school students studying advanced algebra and recurrence relations.

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