If within 45 days from the effective date of the annexation, the city and township from which the territory was detached cannot agree to a joint resolution as provided in section 2, an official special census shall be taken of the area detached from the township and of the entire township from which the area was detached. The census shall be taken by enumerators appointed by the secretary of state upon application of either the city or township. Each enumerator appointed to take such census shall receive for his services not to exceed $10.00 per day, together with his actual and necessary expenses therefor which sum shall be paid by the city or township within which the services of such enumerator were rendered. The ratio of population between the areas detached from the township and the remainder of the township shall be the basis for determination of the pro rata share of the state funds, moneys or grants to be distributed. The township from which the territory was detached or the county agency receiving the funds, moneys or grants in respect of population in the township shall be liable to the city for its proper pro rata share of any state funds, moneys or grants received by the township or county agency after the date of the annexation.