Multiple choice

Two beakers contain two solutions A and B in the ratios 7 : 3 and 2 : 3. The contents of the two beakers are mixed in a third beaker such that the new mixture in the third beaker in the end is in the ratio 3 : 2. Find the ratio in which the contents of both beakers must be mixed.

  1. 2 : 1

  2. 1 : 2

  3. 3 : 1

  4. 4 : 1

  5. 5 : 1
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A Correct answer
Explanation

Using alligation on one component (e.g., the first part of the ratio): Beaker A has 7/10, Beaker B has 2/5 (or 4/10), and the mixture has 3/5 (or 6/10). The difference between A and mixture is |7/10 - 6/10| = 1/10. The difference between B and mixture is |4/10 - 6/10| = 2/10. The ratio is 2/10 : 1/10 = 2 : 1.

AI explanation

Using the rule of alligation on the fraction of compound A in each beaker, the first beaker has 7/10 and the second has 2/5, while the target mixture has 3/5. This sets up the calculation (3/5 - 2/5) : (7/10 - 3/5), which simplifies to 1/5 : 1/10. Therefore, the required ratio of the contents from the first beaker to the second beaker is 2 : 1.

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