Whenever the expense of constructing or repairing any public work placed under the control of the board of public works shall not exceed the sum of 200 dollars, the work shall be done by such board in such manner as they may deem proper; but whenever such expense shall exceed the sum of 200 dollars, then the said board shall submit the plans, diagrams, profiles and estimates thereof to the council for their approval, and when so approved the board shall, subject to the approval of the council, cause such work to be done by contract, or otherwise in such manner as they may deem proper: Provided, That if the expense shall exceed the sum of 500 dollars, the board shall advertise for sealed proposals, and shall give such notice as the council may direct, and shall let the contract to the lowest responsible bidder who shall be deemed competent to do the work and give adequate security for the performance thereof, which contract and security shall be approved by the council.