Sum of digits problem

The maximum carry is 1.This implies the only carries in 2x are the ones accounted for in S(2d) for each digit d in the decimal representation of x.Hence S(2x)= $\sum$ S(2d),where the sum is taken over all the digits of x.It is clear that $\frac{S(d)}{S(2d)}$ <= 5 for every decimal digit d not equal to 0.Thus $\frac{S(x)}{S(2x)}$ <=5.The equality holds if x=5 and hence the bound can not be improved. Another way I want u people to think is in the way that S(x)=S(10x)....then????.....10=5*(2x) use and see...want some one to solve in this manner... :).