The number of apples in basket $$A$$ was $$\frac{13}{19}$$ of that in basket $$B$$. After $$10$$ apples were taken out from basket $$A$$ and were put in basket $$B$$, the number of apples in basket $$A$$ became $$\frac{1}{3}$$ of that in basket $$B$$. How many apples were there in basket $$A$$ and basket $$B$$, respectively, in the beginning? ． 
Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems
The total number of apples in basket $$A$$ and basket $$B$$ is constant. In the beginning, $$A: B=13:19$$; now, $$A: B=1:3=8:24$$ (the total number of portions is still $$32$$). By comparison, the number of portions in basket $$A$$ decreases by $$5$$, and the number of portions in basket $$B$$ increases by $$5$$, so each portion is $$10\div5=2\text{kg}$$. Formerly, there were $$13\times2=26$$ apples in basket $$A$$ and $$19\times2=38$$ apples in basket $$B$$. So, the answer is $$C$$. 