A and B are solutions of acid and water. The ratios of water and acid in A and B are (4 : 5) and (1 : 2) respectively. If (x) liters of A is mixed with (y) liters of B, then the ratio of water and acid in the mixture becomes (8 : 13). What is (x : y?)

Solution A has water:acid = 4:5, meaning water is 4/9 and acid is 5/9 of x liters. Solution B has water:acid = 1:2, meaning water is 1/3 and acid is 2/3 of y liters. Mixture ratio is 8:13, meaning water is 8/21 and acid is 13/21 of (x+y) liters. Setting up equations: (4x/9) + (y/3) = 8(x+y)/21 and (5x/9) + (2y/3) = 13(x+y)/21. Solving yields x:y = 3:4. This is a standard mixture problem requiring ratio algebra.