@Akash and @Sreshta
The answer given is Option(C) only. Even I had this doubt earlier why the '=' is required but then reached the following conclusion.
It is already found that the shortest distance between s to v is 65 and s to u is 12. So, yes this is true that w(u,v)>12. But even if we find w(u,v) to be 12, since already the shortest distance is found, it won't get modified. So, we can have w(u,v)>=12. Recall Dijkstra's Algo, once the shortest distance is found, even if the same distance is again obtained, we won't change it. Since we must choose the best answer, (C) is the answer. ((C) and (D) both are true but option (C) is more specific so it's better that (D)).