Two equal glasses are respectively 1/3 and 1/4 full of milk. Each is then filled to the top with water, and the contents are mixed into a tumbler. What is the ratio of milk to water in the tumbler?

Introduction / Context: This is a mixture problem with equal-capacity vessels. Parts of each glass contain milk; the rest is water after topping up. We add both glasses to a tumbler and compute the overall ratio of milk to water.

Given Data / Assumptions:

• Two equal glasses of capacity V.
• Milk volumes: V/3 and V/4 respectively.
• Each is filled to full with water; then the two are mixed.

Concept / Approach: Total milk is the sum of milk from both glasses. Total mixture volume is 2V. Ratio milk:water is milk : (2V − milk).

Step-by-Step Solution: Milk total = V/3 + V/4 = 7V/12. Total mixture = 2V ⇒ water = 2V − 7V/12 = 17V/12. Milk : Water = (7V/12) : (17V/12) = 7 : 17.

Verification / Alternative check: Using any numerical V (e.g., V = 12 units) reproduces the same ratio 7 : 17, confirming independence from absolute capacity.

Why Other Options Are Wrong: 7 : 5, 3 : 7, 11 : 23 are not consistent with the computed volumes 7V/12 milk and 17V/12 water.

Common Pitfalls: Forgetting that the glasses are first topped with water, or assuming unequal capacities. Also, do not average ratios directly; compute actual quantities.

Final Answer: 7 : 17