Concept:Let the two-digit number be 10x+y, and its reverse be 10y+x.Given that the sum of the digits is x+y=9.Explanation:According to the question, twice the number equals 9 times the reversed number.So, 2(10x+y)=9(10y+x).Expanding gives 20x+2y=90y+9x.Rearranging terms: 20x−9x=90y−2y.Thus, 11x=88y, which simplifies to x=8y.Using x+y=9, substitute x=8y: 8y+y=9.So, 9y=9, giving y=1.Then x=8.Therefore, the required number is 10(8)+1=81.Answer:D. 81