Let two digit number is 10x + y

Now, sum of two digit is x + y = 9 ..........1

When we reverse the number, then new number = 10y + x

Now, according to question,

     9(10x + y) = 2(10y + x)

=> 90x + 9y = 20y + 2x

=> 90x - 2x = 20y - 9y

=> 88x = 11y

=> y = 88x/11

=> y = 8x  ............2

From equation 1, we get

     8x + x = 9

=> 9x = 9

=> x = 9/9

=> x = 1

From equation 2, we get

     y = 8*1

=> y = 8

So, the number = 10x + y

                      = 10 * 1 + 8

                     = 10 + 8

                     = 18