Translation:My parents bought their house in the seventies.
In Danish it would be "Mine forældre købte deres hus i halvfjerdserne". There seems to be a difference between Danish and Swedish regarding personal pronouns though. I didn't know about that difference but I found http://www.lardigsvenska.com/2010/11/personliga-promonen.html: "Den gyllene regeln: Sin/sitt/sina med objekt hans/hennes/deras med subjekt"
So you would say: "Deras hus är från sjuttiotalet" (which may or may not be true), but "De köpte sitt hus på sjuttiotalet".
I actually like the Swedish form better than the Danish. The Swedish plural form is more consistent with the singular form, and it's less ambiguous. For example in Danish you would say "Han købte sit hus" (not "Han købte hans hus", unless you're from Jutland :-) ) which is equivalent to the Swedish plural form.
[Edit, the following makes no sense, see Arnauti's comment below] Looking back on the Swedish and English sentences I would claim that "Mina föräldrar köpte deras hus på sjuttiotalet." should be accepted, because the English sentence is ambiguous (if you're a nitpicker). "My parents bought Peter and Mary's house" may or may not be the same as "They bought their house". In Swedish this ambiguity is resolved by using deras/sitt as subject/object.
Don't take my word for it, have a native confirm.
If we translate "Mina föräldrar köpte sitt hus på sjuttiotalet." to Danish it is "Mine forældre købte deres hus i halvfjerdserne" which is why it looked like an error for me to see "sitt" here instead of "deras".
I think duolingonaut and Arnauti should collaborate on making a course of Swedish for Danish speakers and vice versa! I am feeling mildly dyslexic trying to learn Swedish spelling already ;)
In this case you're supposed to translate from Swedish into English, so of course neither sitt nor deras hus is accepted, you must write their house. :P
I guess you're thinking of the reverse version of the sentence, and there both versions are accepted since the English is ambiguous.
I honestly can't really think of a good translation - at least one that's still relevant today. Obviously, every age has its niche words. Maybe fräsigt or something, that sounds really outdated and was in actual use at one time. But if I were to translate "groovy" today, I'd probably just stick to the English equivalent. :)