[Erin]

This is essentially a parallel structure question. It's a hard one, what I call "advanced parallel structure."

Let's take a look...

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
(B) which was determined by when the sun reached the observer’s meridian and which differed
(C) which were determined by when the sun reached the observer’s meridian and differing
(D) determined by when the sun reached the observer’s meridian and differed
(E) determined by when the sun reached the observer’s meridian and differing

The growth of the railroads led to the abolition of local
times, "which were determined by when the sun reached the observer's
meridian and differing"

The growth of the railroads led to the abolition of local
times, "determined by when the sun reached the observer's meridian
and differed"

whats the difference between using ...which were determined...
and ...determined...

is it that - when "which were determined" is used - that
it applies to local times ?
what is similar explanation for the usage of "determined..."

This will be a great help.

A couple of important grammar points here. Let's start with the "original" (without ellipsis, reduction, etc.) sentence:

The growth of the railroads led to the abolition of local times, which were determined by when the sun reached the observer’s meridian and which differed from city to city, and [the growth [of the railroads [also] led] to the establishment of regional times.

This is what the "original" sentence would look like. You will notice that:

which were determined

is parallel with

which differed

These two parts are adjective clauses and can be "reduced" such that they become adjective phrases (or participial phrases in this particular case):

determined

is still parallel with

differing

Okay, that's the first point.

The second point is this:

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

because "were" is the verb for the relative pronoun "which," which replaces the head noun "times."

And I think these two rules should give you answer choice (E).

HTH!!