Multiple choice

The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.

  1. 8%, 16%, 32%

  2. 27%, 9%, 3%

  3. 12%, 24%, 48%

  4. 44%, 22%, 11%

  5. None of these
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C Correct answer
Explanation

Let the percentages be a/r, a, ar. Using weighted averages: (3(a/r) + 2a + 1(ar)) / 6 = 22 and (2(a/r) + 3a + 4(ar)) / 9 = 32. Solving this system yields a=24, r=0.5 or r=2. The sequence is 12, 24, 48.

AI explanation

Assuming the percentages of acid are a, ar, and ar squared, the first mixture condition yields the equation 3a plus 2ar plus ar squared equals 132. The second condition yields 2a plus 3ar plus 4ar squared equals 288. Solving this system of equations gives r equals 2 and a equals 12. Therefore, the percentages are 12 percent, 24 percent, and 48 percent.

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