Two vessels contain milk-water mixtures in ratios 4:1 and 9:11, respectively. If they are combined in the ratio 3:2 by volume, find the milk : water ratio in the resulting mixture.

Introduction / Context:
When mixing mixtures, compute the absolute milk and water contributed from each vessel and then add them according to the given mixing ratio. Finally, express the totals as a simplified milk : water ratio.

Given Data / Assumptions:

• Vessel A: milk : water = 4 : 1 ⇒ milk fraction = 4/5.
• Vessel B: milk : water = 9 : 11 ⇒ milk fraction = 9/20.
• Mixture proportions A : B = 3 : 2.

Concept / Approach:
Take notional volumes: 3 units from A and 2 units from B. Compute milk and water amounts using fractions, add them, and form the final ratio milk : water.

Step-by-Step Solution:
Milk from A = 3 * (4/5) = 12/5; water from A = 3 * (1/5) = 3/5. Milk from B = 2 * (9/20) = 18/20 = 9/10; water from B = 2 * (11/20) = 22/20 = 11/10. Total milk = 12/5 + 9/10 = 24/10 + 9/10 = 33/10. Total water = 3/5 + 11/10 = 6/10 + 11/10 = 17/10. Milk : Water = (33/10) : (17/10) = 33 : 17.

Verification / Alternative check:
The total milk fraction = 33/(33+17) = 33/50, which is consistent with intermediate calculations.

Why Other Options Are Wrong:
34:16 and 16:34 are not supported by the computed fractions; 17:33 reverses the roles of milk and water.

Common Pitfalls:
Averaging ratios directly without converting to actual fractions and volumes. Always compute component amounts before forming the final ratio.

Final Answer:
33 : 17