The growth of the railroads led to the abolition of local times, which was determined by when the sun reached the observer's meridian and differing from city to city, and to the establishment of regional times.



(A) which was determined by when the sun reached the observer's meridian and differing

Local times- plural subject needs a plural verb. Eliminate. 


(B) which was determined by when the sun reached the observer's meridian and which differed

What does the second “which” relate to? Local times?  Observer’s meridian?


(C) which were determined by when the sun reached the observer's meridian and differing

“which were determined… “ is a clause. It is not parallel to “differing” 


(D) determined by when the sun reached the observer's meridian and differed

Determined by functions as a modifier that modifies local times. “differed” functions as verb and not a participle. To make “differed” a participle, we change it to  v+ing- “differing”


(E) determined by when the sun reached the observer's meridian and differing


E is correct. Both “determined” and “differing” function as modifiers.