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?

• A. $1:3$
• B. $2:3$
• C. $3:2$
• D. $5:3$

Answer 1

The correct option is D $5:3$

Milk in first glass $=\frac{1}{2}$ unit

Milk in second glass $=\frac{3}{4}$ unit

Water in first glass $=\frac{1}{2}$ unit

Water in second glass $=\frac{1}{4}$ unit

Therefore, the required ratio is as follows:

$\frac{\frac{1}{2}+\frac{3}{4}}{\frac{1}{2}+\frac{1}{4}}=\frac{\frac{2}{4}+\frac{3}{4}}{\frac{2}{4}+\frac{1}{4}}=\frac{\frac{2+3}{4}}{\frac{2+1}{4}}=\frac{\frac{5}{4}}{\frac{3}{4}}=\frac{5}{4}\times \frac{4}{3}=\frac{5}{3}=5:3$

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