# Rotating digits of a three digit number.

Let us consider a three digit number $$\overline{a b c}$$.

If 9 is added to this number, it becomes $$\overline{a c b}$$, and let this be called ‘new number’.

If 90 is added to the ‘new number’, it becomes $$\overline{c a b}$$.

What is the sum of the largest possible number and the smallest possible number of this type?