I was wondering that myself. Made me think it was meant to be "Who answers on such a question?". A little unusual way to phrase it, but not wrong in English (afaik).
It's like jbrains762 said, either besvara or svara på. With svara + question, the preposition is compulsory. (You say Jag svarar henne 'I answer her', so the recipient of the answer does not need a preposition, only the question).
It seems to me that 'answer on such a question' has a slightly different meaning in English.
I've never heard "answer on" in English and would never expect it. At most, perhaps, "Who answers, upon hearing such a question?" which means something altogether different.
Who answers to such a question? sounds better but idk if på could be translated like this.
På can be translated as all sorts of English prepositions, I find; the correspondence with prepositions is usually tricky.
Does sådan always come after the adjective? And will "Vem svarar på sådan fråga" imply yhe same thing? It just feels weird when saying "en sådan fråga".