$\frac{55^{3}+45^{3}}{55^{2}- 55 \times 45 + 45^{2}}$
We know that
$\therefore (a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}))$
$ (a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
So,
$=\frac{(55+45)(55^{2}-55 \times 45+45^{2})}{(55^{2}-55 \times 45+45^{2})}$
$=(55+45)$$=100$
Hence,Option(A)100.