When the control and administration of any matter is by or under this Act transferred to a district board, and at the time of the transfer the cost of that control and administration is defrayed from provincial revenue, the Local Government shall, from time to time, allot to the district board such funds, .or place at the disposal of the board such sources of income, as may, in the opinion of the Local Government and of the board, be sufficient for maintaining the control and administration of the said matter in the state of efficiency existing at the date of transfer.