Bucket A has a number of kilograms of pure water, bucket B has a number of kilograms of pure alcohol, the first time from the bucket A to the bucket B pouring water, so that the bucket B

bucket A bucket A bucket B bucket B

Total mass Water mass Total mass Alcohol mass

(1) X-Y X-Y 2Y Y

(2) X-Y/2 X-Y/4 3Y/2 3Y/4

(3) 4X/5 -2Y/5 4X/5 -3Y/5 X/5 +7Y/5 4Y/5

Based on the fact that the mass of the liquid in the final bucket A is exactly equal to the mass of the liquid in the initial bucket B, 4/5X-2/5Y= Y, we have

X=7/4Y

Bucket A: Concentration of water = (4Y/5)/Y=80%, concentration of alcohol = (Y/5)/Y=20%

Bucket B: water concentration = (19Y/20)/(7Y/4) = 54.29%, alcohol concentration = (4Y/5)/(7Y/4) = 45.71%