A large container has a 50 litre mixture of juice and water in the ratio 3 : 2. To this, a 60 litre juice and water mixture is added, that has a juice to water ratio of 2 : 1. After this, 11 litres of the solution is replaced with pure juice. What is the ratio of water to juice in the final mixture?

Juice in first container: $$\dfrac{3}{5} \times 50 = 30 \text{ litres}$$

Water in first container: $$\dfrac{2}{5} \times 50 = 20 \text{ litres}$$

Now, a $$60$$ litre mixture with a juice to water ratio of $$2:1$$ is added.

So, Juice in this mixture:$$\dfrac{2}{3} \times 60 = 40 \text{ litres}$$

Water in this mixture: $$\dfrac{1}{3} \times 60 = 20 \text{ litres}$$

Combining the two:

Total Volume: $$50+60=110\text{ litres}$$

Total Juice: $$30 + 40 = 70 \text{ litres}$$

Total Water: $$20 + 20 = 40 \text{ litres}$$

So, Juice to Water Ratio: $$70:40 = 7:4$$

Now, when $$11$$ litres of the solution is removed, it is removed in the current ratio of the mixture ($$7:4$$).

Juice removed: $$\dfrac{7}{11} \times 11 = 7 \text{ litres}$$

Water removed: $$\dfrac{4}{11} \times 11 = 4 \text{ litres}$$

Juice remaining: $$70 - 7 = 63 \text{ litres}$$

Water remaining: $$40 - 4 = 36 \text{ litres}$$

Final Juice: $$63 + 11 = 74 \text{ litres}$$

Final Water: $$36 \text{ litres}$$

Water : Juice = $$36 : 74$$ = $$18 : 37$$