Multiple choice

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

  1. 4 : 5

  2. 3 : 5

  3. 5 : 3

  4. 5 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A be acid, W be water. (A)/(W+2) = 1. (A+15)/(W+2) = 4. Solving gives A=5, W=3. Ratio W:A = 3:5.

AI explanation

Let the original quantities of acid and water be A and W, with a total volume V. Adding 2 litres of water makes the acid concentration 50%, so A divided by (V + 2) equals 0.5, meaning A equals W + 2. Adding 15 litres of acid to this new mixture makes the concentration 80%, so (A + 15) divided by (V + 2 + 15) equals 0.8. Substituting A with W + 2 gives (W + 17) divided by (V + 17) equals 0.8; since V equals 2W + 2, we get (W + 17) divided by (2W + 19) equals 0.8, which solves to W = 3. Substituting W back into A = W + 2 gives A = 5, making the original ratio of water to acid 3:5.

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