Multiple choice

Two vessels of equal capacity contain water and alcohol. The first vessel, containing alcohol, is filled up to its maximum capacity, and the second vessel, containing water, is two-thirds empty. The content of the first vessel is poured into the second vessel to fill it to capacity and then the content of the second vessel is poured into the first vessel until it is full, and then again, the content of the first vessel is poured into the second vessel to fully fill it up. If we repeat the operation fourth time such that the first container is half-filled by pouring the content of the second container into it, then what will be the ratio of alcohol to water in the first container?

  1. 60 : 19

  2. 62 : 19

  3. 19 : 62

  4. 19 : 60

  5. 17 : 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a complex vessel transfer problem. Following the steps carefully: Vessel 1 (V1) starts full of alcohol, Vessel 2 (V2) is 1/3 full of water. After the sequence of pours described, the ratio of alcohol to water in the first container is 62:19.

AI explanation

Let the capacity of each vessel be 1 unit. Initially, vessel 1 has 1 unit of alcohol and vessel 2 has 1/3 unit of water. The process involves repeated mixing and transferring until the fourth operation. After tracing the exact quantities of water and alcohol throughout the successive transfers, the first container ends up with 62 parts alcohol for every 19 parts water.

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