Multiple choice

A flask contained a mixture of wine and water. It contained 30% wine and the rest was water. A person removed some part of the mixture and replaced it with another wine-water mixture, in which the wine was only 12%. The new mixture was then found to be containing 18% wine and rest was water. What part of the wine-water mixture was replaced?

  1. 2 3

  2. 1 3

  3. 1 2

  4. 5 6

  5. 7 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation between the initial mixture (30% wine) and the replacing mixture (12% wine) to get the final mixture (18% wine): the ratio of initial mixture to replaced mixture is (18 - 12) : (30 - 18) = 6 : 12 = 1 : 2. This means 2 parts out of 3 parts total were replaced. Option A shows '2 3' representing 2/3.

AI explanation

This is a replacement problem where the initial concentration of wine is 30%, the replacing mixture has 12% wine, and the final mixture has 18% wine. Using the formula (Initial Amount - Replaced Amount) / Initial Amount = (Final Concentration - Added Concentration) / (Initial Concentration - Added Concentration), we get the replaced fraction as 1 - (18 - 12) / (30 - 12). This simplifies to 1 - (6/18), which equals 1 - 1/3, resulting in a replaced part of 2/3. The required part is 2/3.

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