Multiple choice

A container contains a mixture of Spirit 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 Spirit and Water of the resultant mixture in the container becomes 1 : 1?

  1. 1/3

  2. 2/3

  3. 3/4

  4. 4/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial ratio 3:1 (Spirit:Water). Let total volume be 4 units (3 spirit, 1 water). Removing fraction 'f' leaves 3(1-f) spirit and 1(1-f) water. Adding 'f' of water makes spirit 3(1-f) and water 1(1-f) + 4f. Set 3(1-f) = 1(1-f) + 4f. 3 - 3f = 1 - f + 4f. 2 = 6f. f = 1/3.

AI explanation

If the initial spirit fraction is 3/4 and the desired spirit fraction is 1/2, then substituting a fraction x of the mixture with water maintains the amount of spirit but changes the total mixture fraction. The equation for the final spirit fraction is (3/4) times (1 minus x) equals 1/2. Solving for x gives 1 minus x equals 2/3, which means x is 1/3. The fraction of the mixture that must be drawn off and substituted is 1/3.

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