Whenever, in the opinion of the board of managers of any house of refuge or reform school in this Commonwealth, it shall be for the best interests of any minor committed to it, that he or she shall leave the institution on parol,¹ and there is no relative or guardian fit or capable of assuming the custody or care of such minor, and such minor is through mental or physical defects unfit to be indentured or placed out on wages or for a home, and it is necessary that board shall be paid to secure a home, it shall be lawful for such house of refuge or reform school to pay such board as may be necessary, not exceeding in any case the current per capita charge, one-half of which is paid by the counties from which children are committed to such institution, and to charge the amount so paid to the current expenses of the institution; and in the charges made to the county from which such minor has been committed, he or she shall be counted as an inmate from such county so long as he or she shall remain under the guardianship of such house of refuge or reform school.