Multiple choice

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 it with water is repeated three more times, then the final ratio of milk to water in the glass, is

  1. 1 : 26

  2. 1 : 80

  3. 1 : 27

  4. 1 : 81
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After each replacement, the fraction of milk remaining is (1 - 2/3) = 1/3. After 4 operations (initial + 3 repeats), the fraction of milk is (1/3)^4 = 1/81. The ratio of milk to water is 1 : (81-1) = 1 : 80.

AI explanation

Using the formula for repeated replacement, the final quantity of milk is Initial Milk times (1 minus the fraction removed) raised to the number of times the process is done. The process is done four times, so the fraction of milk remaining is (1 minus 2/3) raised to the power of 4, which is 1/3 to the power of 4, or 1/81. If the total mixture is 1, the milk is 1/81 and the water is 80/81. The final ratio of milk to water is therefore 1 to 80.

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