Multiple choice

Two beakers A and B, both contain two solutions, ethanol and methanol, in the ratio 14 : 6 and 4 : 6, respectively. If the contents of these two beakers are mixed together in a third beaker, such that the new mixture in the third beaker is in the ratio 6 : 4, then find the ratio in which the content of both the beakers A and B must be mixed, respectively.

  1. 1 : 2

  2. 1 : 3

  3. 2 : 1

  4. 3 : 2

  5. 4 : 1
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C Correct answer
Explanation

Beaker A ratio is 14:6 (7:3), Beaker B is 4:6 (2:3). Let the mixture ratio be x:y. Using the allegation method on the ethanol fraction: (7/10)x + (2/5)y = (6/10)(x+y). This simplifies to 0.7x + 0.4y = 0.6x + 0.6y, leading to 0.1x = 0.2y, or x/y = 2/1.

AI explanation

Using the rule of alligation on the ethanol fractions, beaker A has a concentration of 14/20 (or 0.7) and beaker B has a concentration of 4/10 (or 0.4). The desired mixture has an ethanol concentration of 6/10 (or 0.6). Calculating the ratio as (0.6 - 0.4) to (0.7 - 0.6) gives 0.2 to 0.1. Therefore, the required mixing ratio of beaker A to beaker B is 2 : 1.

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