If $$a=1$$, $$b=2$$, and $$c=3$$, then $$\overline{abc}=123$$. Given that $$A=\overline{xy}$$ and $$B=\overline{2xy}$$, if $$B$$ is $$25$$ more than six times of $$A$$, what is the value of $$A$$?  John attempted to answer the question in this way:  Since we have that $6\times \overline{xy}+25 = \overline{2xy}$, then $60x+6y+25=200+10x+y$ which implies that $10x+y =45$ and so $\overline{xy} = 45$.  Is he right or wrong? If not, solve for the correct answer. 
Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value