Solution A is made up of alcohol and water mixed in the ratio of 21 : 4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2 : 3 by volume. If Solution A and Solution B are mixed in the ratio of 5 : 6 by volume, what percent of the resultant mixture is alcohol?

Question: Solution A is made up of alcohol and water mixed in the ratio of 21 : 4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2 : 3 by volume. If Solution A and Solution B are mixed in the ratio of 5 : 6 by volume, what percent of the resultant mixture is alcohol?

Solution:
25 units of A contain 21 units of alcohol and 4 units of water.
So, 5 units of A contain (21/5) units of alcohol and (4/5) units of water
5 units of B contain 2 units of alcohol and 3 units of water

If we mix 5 × 5 = 25 units of A with 5 × 6 = 30 units of B (so that A and B are mixed in the ratio of 5 : 6), the resultant 55 units solution will contain:
Alcohol: (21/5) × 5 + (2 × 6) = 33 units
Water: (4/5) × 5 + (3 × 6) = 22 units

% of alcohol in the resultant solution = (33/55) × 100 = 60