Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to

Question

Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?

Accepted Answer

Let the volume of each glass be V.

Glass 1:
Milk = V/2
Water added to fill = V - V/2 = V/2

Glass 2:
Milk = 3V/4
Water added to fill = V - 3V/4 = V/4

When contents are poured into another vessel:
Total Milk = Milk from Glass 1 + Milk from Glass 2
Total Milk = V/2 + 3V/4 = 2V/4 + 3V/4 = 5V/4

Total Water = Water from Glass 1 + Water from Glass 2
Total Water = V/2 + V/4 = 2V/4 + V/4 = 3V/4

Ratio of Milk to Water = (Total Milk) : (Total Water)
Ratio = (5V/4) : (3V/4)
Ratio = 5:3

Therefore, the ratio of milk to water in the vessel is 5:3.

Option A (1:3): Incorrect. This would imply much less milk relative to water.
Option B (2:3): Incorrect. This would mean 2 parts milk for 3 parts water.
Option C (3:2): Incorrect. This would mean more milk than water, but not the correct proportion.
Option D (5:3): Correct. This matches our calculation of 5 parts milk to 3 parts water.

Answer

1:3

Answer

2:3

Answer

3:2

Answer

5:3

Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?

Explanation

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