Question

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

• A. 1:80
• B. 1:27
• C. 1:26
• D. 1:81

Answer 1

The Correct Option is A

We can solve this using the "successive dilution" method. Imagine the glass initially holds 1 unit of milk.

Iteration 1: Pour out two-thirds of the milk, leaving one-third. The milk remaining is:

Remaining Milk = Initial Milk × (1/3) = 1 × (1/3) = 1/3Nbsp;

Refill the glass with water to the 1-unit mark. The total volume remains 1 unit, but the milk concentration changes.

Iteration 2: Repeat the process:

Remaining Milk = (1/3) × (1/3) = 1/9

Iteration 3:

Remaining Milk = (1/9) × (1/3) = 1/27

Iteration 4:

Remaining Milk = (1/27) × (1/3) = 1/81

After four iterations, the milk fraction is 1/81. The rest is water, so the water fraction is:

Water Fraction = 1 - Milk Fraction = 1 - (1/81) = 80/81

The final milk-to-water ratio is 1:80, confirming 1:80 is the correct answer.