Multiple choice

Two vessels A and B contain mixtures of acid and water in the ratios of 4 : 3 and 5 : 3 respectively. Find the ratio in which these mixtures should be mixed to obtain a new mixture in vessel C containing acid and water in the ratio of 3 : 2.

  1. 5 : 8

  2. 7 : 8

  3. 7 : 5

  4. 4 : 7
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B Correct answer
Explanation

Using the allegation method on the acid content: Vessel A has 4/7, Vessel B has 5/8, and the mixture has 3/5. The differences are |5/8 - 3/5| = 1/40 and |4/7 - 3/5| = 1/35. The ratio is (1/40) : (1/35) = 35 : 40 = 7 : 8.

AI explanation

The fraction of acid in vessel A is 4 divided by 7, in vessel B is 5 divided by 8, and in vessel C is 3 divided by 5. Applying the rule of alligation, the ratio of the quantities of mixtures from A and B is (5 over 8 minus 3 over 5) to (3 over 5 minus 4 over 7). Solving the fractions gives the ratio 1 over 40 to 1 over 56, which simplifies by multiplying both sides by 280 to yield 7 to 8.

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