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A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture becomes half water and half syrup?

1. 1/3
2. 1/4
3. 1/5
4. 1/7

Correct answer: 1/5

Solution

Initially, syrup forms 5/8 of the mixture. If x of the mixture is removed and replaced with water, the syrup left becomes (1 - x) times the original syrup fraction. Set (5/8)(1 - x) = 1/2 and solve for x.

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