Multiple choice

Two chemical solutions X and Y are mixed in the ratio 7 : 3, respectively. Solution X contains m% of acid and n% of water, while solution Y contains o% of acid and p% of water. When solution X is combined with solution Y, the final percentage of acid in the total mixture becomes 40% of the total volume. If m - o = 40, find m : o.

  1. 3 : 25

  2. 13 : 3

  3. 20 : 17

  4. 7 : 20

  5. 8 : 23
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B Correct answer
Explanation

Let V be total volume. Acid from X = 0.7V * (m/100), Acid from Y = 0.3V * (o/100). Total acid = 0.4V. So, 0.7m + 0.3o = 40. Given m - o = 40, substitute o = m - 40: 0.7m + 0.3(m - 40) = 40 => 0.7m + 0.3m - 12 = 40 => m = 52. Then o = 12. Ratio m:o = 52:12 = 13:3.

AI explanation

Using the method of alligation on the acid percentages of solution X (m%) and solution Y (o%), the ratio of quantities is (40 - o) : (m - 40). We are given this ratio is 7 : 3, so 3(40 - o) = 7(m - 40), which simplifies to 7m + 3o = 400. We are also given m - o = 40, meaning o = m - 40. Substituting this into the first equation gives 7m + 3(m - 40) = 400, resulting in 10m = 520 and m = 52. Therefore, o = 12, making the required ratio 52 : 12, which simplifies to 13 : 3.

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