During such time as grants-in-aid are provided or made available by the United States government for either direct costs or administrative costs of welfare activities under this chapter, or both, the State Treasurer shall transfer the sums so granted to the Relief Fund. Of such sums, there shall be credited to the state an amount which bears the same proportion to the total of the sums so granted that the total state expenditure under this chapter during the period for which the grants are made bears to the total of both state and county expenditures under this chapter during that period. The remainder of such sums shall be credited to the counties of the state, and the State Treasurer shall pay to each county therefrom an amount which bears the same proportion to the whole of such remainder that the county funds expended by that county under this chapter during the period bears to the total of all county funds expended by all counties under this chapter during the period.