OE - B, and E

The detour road sign "rather than" indicates that the has one of two contrasting qualities: "diligence" ("thoroughness") rather than "celerity" ("speed"). He is not quick, yet he is thorough. The chef initially disliked the busboy's work habits, but the detour road sign "though" indicates that she has come to like them, since thoroughness can be more important than rapidity. For the first blank, you need a word that means something like thoroughly. Choice (B) sedulously, which means "perseveringly," works well. Choice (A) perfunctorily, "superficially," is the opposite of what you need, and (C) desperately doesn't make any sense in this context. There is more information available on the second blank. The word "rather" appears again as a detour road sign. The sentence mirrors the earlier contrast in the question. The chef has come to appreciate the busboy's thoroughness even though the busboy isn't fast. Choice (E) expediently means "quickly," and matches the prediction perfectly. Choice (D) haphazardly means "sloppily," which is not a quality the chef would want. Choice (F) disingenuously means "insincerely," which makes no sense here.

But doesn't expediently mean beneficial and useful(correct me if I'm wrong)? if the word was expeditiously then it would make sense, right?

No because the first term means basically she does not use trick

The second term, basically, means speed.........

the item was expeditiously delivered

regards