Answer 444.444:555.556
Excuse my poor English. I can't explain sufficiently.
In the mixture of beaker A, there is 62.5% of sugar. And in beaker B there is 40% of sugar.
If the new mixture containing half sugar and half water is 1000g, the mixture of beaker A is 444.444g and the mixture of beaker B is 555.556g. (62.5x+40y=500, x+y=1000 ⇒ x=444.444, y=888.889 < in 1000g of new mixture there is 500g of sugar>)
If the new mixture containing half sugar and half water is 2000g, the mixture of beaker A is 888.889g and the mixture of beaker B is 1111.111g.