Multiple choice

CHEMISTRY You combine $2$ solution to form a mixture that is $40\%$ acid. One solution is $20\%$ acid and the other is $50\%$ acid. If you have $90$ milliliters of the mixture, how much of each solution was used to create the mixture?

  1. $20$ mLof solution $A$ and $80$ mL of solution $B$ were used.
  2. $80$ mLof solution $A$ and $70$ mL of solution $B$ were used.
  3. $30$ mL of solution $A$ and $60$ mL of solution $B$ were used.
  4. $40$ mLof solution $A$ and $70$ mL of solution $B$ were used.
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C Correct answer
Explanation

Let the amounts of 20% and 50% acid solutions be a and b millilitres. Since a + b = 90 and 0.20a + 0.50b = 0.40 x 90, solving gives a = 30 and b = 60.

AI explanation

Using the rule of alligation, the ratio of the 20% acid solution to the 50% acid solution is (50 - 40) : (40 - 20), which equals 10 : 20 or 1 : 2. The total parts are 3, corresponding to the 90 milliliters of mixture, meaning 1 part equals 30 milliliters. Therefore, 30 mL of the 20% solution (solution A) and 60 mL of the 50% solution (solution B) were used.

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