Explanation:

- Start with a 120-liter mixture of milk and water in the ratio 17:7.

- This means there are 85 liters of milk (17/24 of 120) and 35 liters of water (7/24 of 120).

- 40% of this mixture is poured out: 48 liters total (40% of 120).

- In the 48 liters, there are 34 liters of milk (17/24 of 48) and 14 liters of water (7/24 of 48).

- Pour this into vessel X, which already has a 100-liter mixture of milk and water in equal parts (50 liters each).

- After pouring, vessel X has a total of 84 liters of milk (34 from the mix and 50 from X) and 64 liters of water (14 from the mix and 50 from X).

- Thus the new ratio of milk to water is 84:64, which simplifies to 21:16.

- Option 2: 21 : 16 is the correct answer.