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Explanation:

Let the capacity of each cup be 100 ml. So 300 ml of alcohol is taken out from the first container and poured into the second one. So the first vessel will have 200 ml of alcohol and the second one will have 500 ml of water and 300 ml of alcohol. So the ratio of water to alcohol in the second vessel is 5 : 3.
Hence, proportion of alcohol in B = 3 : 8
Now if 300 ml of mixture is removed from the second container, it will have $\left(300\times \frac{5}{8}\right)$ = 187.5 ml of water and $\left(300\times \frac{3}{8}\right)$ = 112.5 ml of alcohol. Now if this mixture is poured in the second vessel, that vessel would have (200 + 112.5) = 312.5 ml of alcohol and 187.5 ml of water. Hence, ratio of alcohol to water in this container = 312.5 : 187.5 = 5 : 3
Hence, proportion of water = A = 3 : 8
Hence, we find that A = B
Note: This result will be independent of the capacity of the cup.