Multiple choice

In a laboratory, two different chemical solutions, solution X and solution Y, are being used in an experiment. Solution X contains a mixture of chemical A and chemical B in the ratio of 3 : 7, while solution Y contains the same chemicals in the ratio of 2 : 5. A scientist needs to mix these two solutions in such a way that the resulting mixture has the ratio of chemical A to chemical B as 5 : 12. If the scientist decides to mix m liters of solution X with n liters of solution Y, then m : n =

  1. 7 : 5

  2. 5 : 7

  3. 10 : 7

  4. 7 : 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solution X has A:B = 3:7 (fraction A = 3/10). Solution Y has A:B = 2:5 (fraction A = 2/7). Mixture has A:B = 5:12 (fraction A = 5/17). Using alligation: |2/7 - 5/17| / |3/10 - 5/17| = |(34-35)/119| / |(51-50)/170| = (1/119) / (1/170) = 170/119 = 10/7.

AI explanation

Using the rule of alligation on the fraction of chemical A in each solution, solution X has 3/10 A, solution Y has 2/7 A, and the target mixture has 5/17 A. The required ratio of X to Y is (5/17 - 2/7) : (3/10 - 5/17). This gives (35 - 34)/119 : (51 - 50)/170, which simplifies to 1/119 : 1/170. Inverting and multiplying by the least common multiple of 119 and 170 gives 170 : 119, which is 10 : 7.

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