Multiple choice

If a 62 ml of liquid contains 8% of component A, how much liquid must be added in order to form a 5%-component A solution?

  1. 41.4 ml

  2. 37.2 ml

  3. 34.3 ml

  4. 29.8 ml

  5. 26 ml
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Amount of A = 0.08 * 62 = 4.96 ml. Let x be the amount of liquid added. New total volume = 62 + x. New percentage = 4.96 / (62 + x) = 0.05. 4.96 = 0.05(62 + x) => 4.96 = 3.1 + 0.05x => 1.86 = 0.05x => x = 37.2.

AI explanation

We can use the rule of alligation by treating the pure liquid being added as having a 0 percent concentration of component A. The ratio of the original liquid to the added liquid is (5 percent minus 0 percent) to (8 percent minus 5 percent), which equals 5 to 3. Since 5 parts correspond to the original 62 ml, 1 part is equal to 12.4 ml. The amount of liquid to be added represents 3 parts, so we multiply 12.4 ml by 3 to get 37.2 ml.

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