Question 42783
Let the cans initially contain 'u' and 'v' amounts of water respectively.


As Jim pours ,from X, as much water into Y as Y already contains so after the first operation, X contains (u-v) and Y contains (v + v =) '2v' amount of water.


Next, he pours 'v' amount of water from Y into X (as presently Y has 'v' amount of water).
So volume of water in Y becomes 'v' and amount of water in X becomes (u-v) + v = u.


Again, Jim pours 'v' amount of water into Y (as presently Y has 'v' amount of water).
So volume of water in Y becomes '2v' and amount of water in X becomes (u-v).
These are the final amounts of water present in X and Y.
Final content in each vessel is 24 ounces.


Thus we have two equations: 
u - v = 24 and 2v = 24.
The equation: 2v =24 gives v = 24/2 = 12.
Then from u - v = 24 we get u = 24 + v = 24 + 12 = 36.


As the initial contents of the vessels were 'u' and 'v' so they contained 36 and 12 ounces of water respectively.