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

Answer: (A)

1:80

Answer 2

Let the initial amount of milk be 1. After the first step, the amount of milk remaining is $\frac{1}{3}$. In each subsequent step, two-thirds of the content is replaced, so the amount of milk remaining after each step follows the pattern:

Milk after step 1 $= \frac{1}{3}$,

Milk after step 2 $= \frac{1}{9}$,

Milk after step 3 $= \frac{1}{27}$,

Milk after step 4 $= \frac{1}{81}$

Thus, the final amount of milk is $\frac{1}{81}$ and the remaining content is water. Theratio of milk to water is 1 : 80.