I bought some books which has upset my budget.
I bought some books which have upset my budget.
The first has the use of 'has'that doesn't agree with the its subject "books". But this sentence has been the part of a text book for decades. I want to know I it's correct. If yes, how? In the second example the helping verb "have" agrees the subject "books" and it seems correct. So, which example is correct and why?
The subject in the first sentence is understood to be "Buying some books" (a partiple/gerund subject). Participles are treated as singular.
The subject in relative clauses, particularly non-restrictive clauses that are separated by a comma, sometimes has to be understood from context. This can create ambiguities. In this case, the singular agreement helps resolve the ambiguity. A comma before "which" would also help.
In the second sentence, the subject would be "books", but that doesn't work well, since the books can't upset a budget.
Consider "I bought a book, which upset my sister." It's ambiguous whether the book, or the fact that I bought the book, caused the upset. However, although it's ambiguous, it probably doesn't matter. We understand the narrative either way.