Any city shall have the power to acquire, establish, erect, equip, operate, and maintain motor vehicle testing stations therein, to pay for the same out of the proceeds of the collection of fees charged for testing motor vehicles, and to make rules and regulations for the purpose of carrying out the provisions of any ordinance adopted under the terms of this chapter. Such city may also designate privately operated stations as official inspecting stations on which such city shall by agreement with the owners or operators of such stations impose the power and authority to conduct such inspections in lieu of or in addition to the stations operated by such city and in accordance with the terms of this chapter and any ordinance adopted under its provisions.