Confusing use of ずつ

Question

このバスの会社によると、東京では１週間に３日、昼と夜の２回ずつ走る予定で、予約が必要です。
According to the company that runs these buses, they plan to run the Tokyo bus three times a week, twice each in the afternoon and evening. A reservation will be needed.

I'm unsure of how to understand 昼と夜の２回ずつ. Does this mean twice in the afternoon and twice in the evening, or does it mean once in the afternoon and once in the evening (making two times in total)?

I'm not even sure whether ずつ modifies 2回 or 3日.

Whichever is the correct interpretation how would you adjust it to give the other one?

Answer 1

昼と夜に2回ずつ is ambiguous, but usually means "twice in the afternoon and twice in the evening", i.e., four times a day.

昼と夜の2回ずつ is not ambiguous and it only means "twice a day, one in the afternoon and one in the evening." Here の is an apposition marker, and 2回 and 昼と夜 are referring to the same thing. ずつ is used in relation to 日 before 昼と夜 (it's "per day" rather than "per 昼と夜").

Answer 2

According to A Dictionary of Basic Japanese Grammar, page 572:

ずつ: a particle that indicates equal distribution of quantity.

Example(s):
私は子供達に本を二冊ずつやった。
I gave two books to each of the children.

[...]

A sentence without ずつ can express virtually the same fact.

昼と夜の２回
2 times, one in the morning, another in the evening.