It shall be the duty of said board to keep books of account, showing with entire accuracy contemporaneous current entries of the receipts and expenditures of the board in such manner as to enable the same to be understood and investigated, and also to preserve on file in its office duplicate vouchers for all its expenditures, which books and duplicates shall at all times be open to the examination of the finance committee of the city council, or any other committee appointed by the common council, and such board shall make such reports of its business and transactions to the mayor and city council of such city, town or village as may be provided by ordinance.