Before adopting or rejecting any bid filed under this chapter, the board shall require the engineer for the district to make a careful and detailed statement of the estimated cost of the work. The board may not award the contract to any bidder if the engineer’s estimate prepared under this section exceeds the engineer’s estimate prepared under section 61-35-54 by forty percent or more. If all bids are not rejected, the board shall award the contract to the lowest responsible bidder, upon the basis of cash payment for the work, if the bidder has furnished the certified check or bidder’s bond required under the provisions of this chapter.