Multiple choice

The ratio of wine and water in a drum is $3 : 1$. What part of the mixture is taken out and same amount of water is added to it so that the ratio of wine and water in the mixture become $1 : 1:$?

  1. $\dfrac {1}{4}$
  2. $\dfrac {1}{3}$
  3. $\dfrac {3}{4}$
  4. $\dfrac {2}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial volume be 4 units (3 wine, 1 water). Replacing a fraction x of the mixture with water changes the wine content to 3(1-x). Setting the new ratio 3(1-x) / (1 - 3(1-x)) = 1/1 leads to 3-3x = 1-3+3x, which simplifies to 6x = 5, but checking the standard replacement formula (1-x/V)^n = remaining/total, we find x=1/3 yields the correct ratio.

AI explanation

Let the initial mixture be 4 units (3 wine and 1 water) and let x units be drawn off. Drawing off x units removes 3x/4 wine, leaving 3 - 3x/4 wine. Adding x water brings the water to 1 - x/4 + x = 1 + 3x/4. Equating the final wine and water gives 3 - 3x/4 = 1 + 3x/4, so 2 = 6x/4, meaning x = 4/3. The fraction of the total mixture taken out is (4/3) / 4 = 1/3.

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