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Let's break down the problem step-by-step to determine the capacity of the container.

1. **Initial Setup**: The container is initially filled entirely with milk. Let's call the total capacity of the container \( V \) liters.

2. **First Extraction and Replacement**:
   - 9 liters of milk are removed, so the volume of milk left in the container is \( V - 9 \).
   - These 9 liters are then replaced with water, so the container still has a total of \( V \) liters but now consists of \( V - 9 \) liters of milk and 9 liters of water.

3. **Second Extraction and Replacement**:
   - Another 9 liters of liquid (a mixture of milk and water) are removed. Since the container now has a mixture of milk and water, we need to consider the proportion of each in the mixture at this stage.
   - The amount of milk and water in the container before the second extraction:
     - Milk: \( V - 9 \) liters
     - Water: 9 liters
   - Therefore, the fraction of milk in the mixture is \( \frac{V - 9}{V} \) and the fraction of water is \( \frac{9}{V} \).

4. **Amount of Milk Removed in the Second Step**:
   - Out of the 9 liters removed in the second extraction, the amount of milk removed is \( 9 \times \frac{V - 9}{V} \).
   - The amount of milk left after this removal is:
     \[
     (V - 9) - 9 \times \frac{V - 9}{V} = (V - 9) \left(1 - \frac{9}{V}\right) = (V - 9) \times \frac{V - 9}{V}
     \]



From a container filled with milk, 9 liters of milk are drawn and replaced with water. Next, from the same container, 9 liters are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16:9, then the capacity of the container, in liters, is

Solve a problem involving the replacement method in a container filled with milk. Understand the step-by-step calculation to find the container's capacity given a final milk-to-water ratio of 16:9 after two replacement cycles.

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