The properties are numbers 100 and 102 Gell Street, which are merged to provide nine self-contained flats.
Six of the flats are currently let producing £40,440 per annum with three available for refurbishment/re-letting.
The auction was held online by Mark Jenkinson which says the income when fully let is more than £60,000. The property was one of 27 lots sold in the online auction.