In exercising the above-mentioned powers and duties, the Board of Appeals may, in conformity with Town Law, reverse, affirm or modify the order, requirement, decision or determination appealed from and shall make such order, requirement, decision or determination as ought to be made in the case referred to it. The concurring vote of a majority of the Board of Appeals shall be necessary to reverse any order, requirement, decision or determination of the Building Inspector or to grant a variance, or to decide in favor of the applicant any matter upon which such Board is required to pass.