(b) A local law imposing such a tax shall be effective only during the period that each of the school districts partly within and partly without such city, by a majority vote of the whole number of its school authorities, shall impose an identical tax within that part of its territorial limits outside of such city. Such school authorities are hereby authorized and empowered so to impose such tax, which shall be effective only during the period when the tax imposed by such city on areas of school districts within such city shall be effective.

(c) Taxes so imposed by such a city and by such school districts shall be administered and collected by such city, in the manner provided for in this section and in subpart A of part III of this article. In the case of such administration and collection in areas outside such city, the city and the city officers and employees administering and collecting the tax shall act as agents for the school district or districts which imposed the tax in such areas. In such instances the school authorities of each district and the governing board of such city may enter into an agreement for the administration and collection of such taxes by the city for and on behalf of the school district. Any such agreement shall state the consideration payable to such city for such service and make such other related provisions as the parties thereto shall consider necessary.

(d) Subject to the terms of such agreement, the total net collections from a tax so imposed by such a city and school districts shall be distributed and paid quarterly to the city school district where it is coterminous with or includes the entire city or to all the school districts partly within or wholly within such city.

(e) Except where the city school district is coterminous with the city or includes the entire area of the city, such amounts shall be distributed and paid to the school district or districts partly within or wholly within the city, in accordance with the total average daily attendance for the last preceding school year of pupils residing in each such district and without regard to the location of the school attended.

(f) All actions taken by majority votes of school authorities pursuant to this section shall be deemed resolutions under this article and shall be official records of the school districts in which they are taken. Certified copies thereof forthwith shall be filed in the offices of the city clerk, state department of education, the secretary of state and the state comptroller.