The Department of Revenue is empowered and directed to collect all of the mileage taxes under this chapter. In order to ascertain the mileage traveled in this state by motor vehicles subject to the provisions of this chapter, the Department of Revenue shall prescribe the records to be kept and reports to be made by said contract carriers and common carriers subject to said section; and, on or before the fifteenth day of each month, each such carrier shall file with the Department of Revenue, in accordance with its requirements, a statement verified under oath by the carrier, or by a person having knowledge of the facts and duly designated therefor by the carrier, showing the mileage traveled in this state by each motor vehicle subject to the provisions of this chapter, operated by such carrier during the preceding calendar month, and shall, at the time of filing of such report, pay to the Department of Revenue the mileage tax reflected by it.