Two glasses of equal volume are respectively half-filled and three-fourths filled with milk. Each glass is then filled to the brim by adding water. The contents of both glasses are poured into a single vessel.

Consider the following statements:
Statement I: The total quantity of milk in the vessel is 5/4 of the glass volume.
Statement II: The ratio of milk to water in the vessel is 5:3.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

Two glasses of equal volume are respectively half-filled and three-fourths filled with milk. Each glass is then filled to the brim by adding water. The contents of both glasses are poured into a single vessel.

Consider the following statements:
Statement I: The total quantity of milk in the vessel is 5/4 of the glass volume.
Statement II: The ratio of milk to water in the vessel is 5:3.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

Let the volume of each glass be 1 unit.

Glass 1: Milk = 0.5, Water = 0.5

Glass 2: Milk = 0.75, Water = 0.25

Combined:
Milk = 0.5 + 0.75 = 1.25 units
Water = 0.5 + 0.25 = 0.75 units

Statement I: Total milk = 1.25 = 5/4

Statement I is correct.

Statement II: Ratio of milk to water = 1.25 : 0.75 = 5:3 

Statement II is correct.

Hence, option c is correct.

Ratio and Proportion

Mixtures and Alligations

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