Multiple choice

In a laboratory, two bottles contain mixture of acid and water in the ratio of 2 : 5 in the first bottle and in the ratio of 7 : 3 in the second. The ratio in which the contents of these two bottles should be mixed such that the new mixture has acid and water in the ratio of 2 : 3 is

  1. 4 : 15

  2. 9 : 8

  3. 21 : 8

  4. 1 : 2
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C Correct answer
Explanation

Using the alligation method: Bottle 1 has 2/7 acid, Bottle 2 has 7/10 acid, and the mixture has 2/5 acid. The differences are |7/10 - 2/5| = 3/10 and |2/5 - 2/7| = 4/35. The ratio is (3/10) : (4/35) = (3/10) * (35/4) = 105/40 = 21/8.

AI explanation

Using the method of Alligation on the fractional parts of acid, the first bottle has 2/7 acid and the second has 7/10 acid, while the desired mixture has 2/5 acid. The ratio of their quantities is (7/10 - 2/5) : (2/5 - 2/7), which simplifies to 3/10 : 4/35. Finding a common denominator of 70 gives 21/70 : 8/70, so the required mixing ratio is 21 : 8.

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