Average, Mixture and Alligation Question 3 - CAT 2024
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 of the content and replacing it with water is repeated three more times, then the final ratio of milk to water in the glass is:
Step-by-Step Explanation
Let the total capacity of the glass be 1 unit, initially filled entirely with pure milk.
- First Operation: Pouring out 2 / 3 of the contents leaves 1 − 2 / 3 = 1 / 3 of the original milk in the glass.
- Subsequent Operations: The process is repeated 3 more times, making it a total of 4 independent operations.
Using the successive dilution formula:
Final Fraction of Milk = 1 / 3⁴ = 1 / 81
This means that out of 81 total units of liquid in the final mixture, exactly 1 unit is milk. The remaining volume must be water:
Water Volume = 81 − 1 = 80 units
Ratio of Milk to Water = 1 : 80
Correct Option: B
💡 FundaMakers Tip:
For multi-stage replacement operations where a fixed fraction is repeatedly taken out and replaced, the final concentration of the native liquid scales exponentially. If you remove 2 / 3, you keep 1 / 3. Repeating this n times scales the concentration by (1 / 3)ⁿ. A quick mental calculation of 3⁴ = 81 reveals the final parts structure instantly.