**Problem Solving Approach:**

To solve this problem, we can use the concept of mixture and alligation.

**Step 1: Establish the initial ratio**

Let's assume that the initial volume of milk in the container is M liters and the initial volume of water is W liters.

So, the initial ratio of milk to water is M:W.

**Step 2: First Replacement**

9 liters of the mixture is drawn from the container and replaced with water.

After the first replacement, the volume of milk in the container remains the same, M liters.

However, the volume of water in the container increases by 9 liters, so it becomes W + 9 liters.

The new ratio of milk to water becomes M : (W + 9).

**Step 3: Second Replacement**

Again, 9 liters of the mixture is drawn from the container and replaced with water.

After the second replacement, the volume of milk in the container remains the same, M liters.

The volume of water in the container increases by 9 liters, so it becomes (W + 9) + 9 = W + 18 liters.

The new ratio of milk to water becomes M : (W + 18).

**Step 4: Final Ratio**

According to the given information, the final ratio of milk to water is 16:9.

So, we have the equation: M : (W + 18) = 16 : 9.

**Step 5: Solving the Equation**

To solve the equation, we can use the concept of alligation.

The difference between the first and second terms of the ratio is 16 - 9 = 7.

The difference between the second and third terms of the ratio is (W + 18) - (W + 9) = 9.

The ratio 7:9 can be simplified to 1:1.29 approximately.

So, we have M : (W + 18) = 1:1.29.

Cross multiplying, we get M * 1.29 = (W + 18).

**Step 6: Finding the Capacity of the Container**

Since we need to find the capacity of the container, which is the sum of the volumes of milk and water, we can add M and W to get the total volume.

M + W = (W + 18) / 1.29.

We can simplify this equation to get the value of M + W, which represents the capacity of the container.

**Step 7: Conclusion**

By following the above steps, we can find the capacity of the container by solving the equations derived from the given information. This approach helps us understand the problem, establish the initial ratio, and find the final ratio using the concept of alligation. Finally, we can solve the equations and calculate the capacity of the container.