CAT 2025 Slot 3 QA Question 10: 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 time

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 time

Accepted Answer

In each operation, two-thirds of the mixture is removed. So, one-third of the milk present remains.
The process is done once and then repeated three more times, so it is done $4$ times in total.
Fraction of milk left = $\left(\dfrac{1}{3}\right)^4$
$= \dfrac{1}{81}$
Fraction of water in the final mi

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