Multiple choice

A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?

  1. $1/4$
  2. $1/3$
  3. $3/4$
  4. $2/3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let barrel capacity = 4 units (3 wine + 1 water). To make ratio 1:1, we need 2 wine + 2 water. Remove x fraction: remaining wine = 3(1-x), water = 1(1-x) + x. Set 3(1-x) = 1(1-x) + x. Solve: 3-3x = 1-x+x, so 3-3x = 1, giving 2x=2 and x=1/3. Option A (1/4) is incorrect because it would leave 2.25 wine and 1.75 water.

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