The quorum court in each county shall provide for the collection of delinquent taxes within the county and shall place by ordinance the responsibility therefor in the office of the county collector or the combined office of sheriff and collector, or may provide for the collection of delinquent taxes by a person designated by a board composed of the county judge, an appropriate representative of the public schools in the county, and the mayor of the county seat or of each county seat in the case of those counties having two (2) county seats.