Multiple choice

Mixtures A and B contain alcohol and water. 3 litres of mixture A and 4 litres of mixture B are mixed to get a mixture with 30% alcohol. 4 litres of mixture A and 3 litres of mixture B are mixed to get a mixture with 25% alcohol. In what ratio should we mix the two mixtures A and B to get a new mixture with 27.5% alcohol?

  1. 1 : 2

  2. 1 : 1

  3. 2 : 3

  4. 3 : 4

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Let mixture A have alcohol concentration a and mixture B have concentration b. From the given information, we have 3a + 4b = 2.1 and 4a + 3b = 1.75. Multiplying the first equation by 4 and the second by 3 gives 12a + 16b = 8.4 and 12a + 9b = 5.25, so 7b = 3.15, meaning b = 0.45 or 45%; substituting this back shows a = 0.10 or 10%. To get a 27.5% alcohol mixture using the rule of alligation, the ratio of mixture A to mixture B is (27.5 - 10) : (45 - 27.5), which is 17.5 : 17.5 or 1 : 1.

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