Multiple choice

The ratios of spirit to wine in two flasks labelled as A and B, containing spirit and wine mixture, are 7 : 3 and 3 : 1, respectively. Some amounts of the mixtures from the two flasks are poured into a third flask. The new mixture now contains spirit and wine in the ratio of 11 : 4. Find the ratio in which the mixtures from the flask A and flask B are mixed together to get this new mixture.

  1. A : B = 1 : 2

  2. A : B = 2 : 1

  3. A : B = 1 : 3

  4. A : B = 2 : 3

  5. A : B = 3 : 2
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A Correct answer
Explanation

Using alligation: Flask A has 7/10 spirit, Flask B has 3/4 spirit. The mixture has 11/15 spirit. Difference 1: |11/15 - 3/4| = |44/60 - 45/60| = 1/60. Difference 2: |7/10 - 11/15| = |21/30 - 22/30| = 1/30. Ratio = (1/60) : (1/30) = 1:2.

AI explanation

Convert the given ratios of spirit to total mixture to find their fractional parts. Flask A has a spirit fraction of 7/10, flask B has a spirit fraction of 3/4, and the new mixture has a spirit fraction of 11/15. Using the rule of alligation, the ratio of quantity A to quantity B is (11/15 minus 3/4) to (7/10 minus 11/15), which equals -1/60 to -1/30. Taking the absolute values gives a mixing ratio of 1 : 2.

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