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…

Correct Option (4)

To determine the ratio of milk to water in the combined vessel, we first calculate the individual quantities of milk and water from each glass. Let 'V' represent the equal volume of each glass.

• For the first glass:
  • Quantity of milk = $\frac{1}{2}V$21​V
  • Quantity of water (added to fill the brim) = $V - \frac{1}{2}V = \frac{1}{2}V$V−21​V=21​V
• For the second glass:
  • Quantity of milk = $\frac{3}{4}V$43​V
  • Quantity of water (added to fill the brim) = $V - \frac{3}{4}V = \frac{1}{4}V$V−43​V=41​V

When the contents of both glasses are poured into another vessel:

• Total quantity of milk = $\frac{1}{2}V + \frac{3}{4}V = \frac{2}{4}V + \frac{3}{4}V = \frac{5}{4}V$21​V+43​V=42​V+43​V=45​V
• Total quantity of water = $\frac{1}{2}V + \frac{1}{4}V = \frac{2}{4}V + \frac{1}{4}V = \frac{3}{4}V$21​V+41​V=42​V+41​V=43​V

The ratio of milk to water in the new vessel is:

$$\frac{\text{Total Milk}}{\text{Total Water}} = \frac{\frac{5}{4}V}{\frac{3}{4}V} = \frac{5}{3}$$Total WaterTotal Milk​=43​V45​V​=35​

Thus, the ratio of milk to water is 5 : 3.

Incorrect Options:

Options (1) 1 : 3, (2) 2 : 3, and (3) 3 : 2 are incorrect. These ratios do not align with the precise calculation of the combined quantities of milk and water derived from the problem statement. Any deviation from the calculated total quantities of milk and water would lead to these incorrect ratios.