Option C is the correct answer.
if $_{x \to a}^{lim}$$\frac{f(x)}{g(x)}$ exist then neither $_{x \to a}^{lim}$ f(x) nor $_{x \to a}^{lim}$g(x) may exist.
eg:-
Let f(x) = $_{x \to 0}^{lim}$$\frac{x}{|x|}$ and g(x) = $_{x \to 0}^{lim}$$\frac{x}{|x|}$
Here for both f(x) and g(x) the limit does not exist since LHL $\neq$ RHL.
But $_{x \to 0}^{lim}$$\frac{f(x)}{g(x)} = 1$