What should I do if I saw two old questions being duplicates both having answers and both having an accepted answer? Should I still vote to close one of them? Both?
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By all means vote to close.
It might be worth flagging one of the questions for moderator attention so that they can merge them, though the questions really have to be identical for this to work.
IMHO, the idea behind closing-as-duplicate is to help OP (and future googlers) to get quality answer without reinventing the wheel. From this point of view, closing n months old question already having adequate answer is useless.
Also, it was noted many times by the founders that some amount of duplication is acceptable.