Let the one’s digit be ‘a’ and ten’s digit be ‘b’.

Given, sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits.

⇒ a + b = 9 ----- (1)

Also, 9(10b + a) = 2(10a + b)

⇒ 88b = 11a

⇒ a = 8b

Substituting value of a in eq1

⇒ 9b = 9

⇒ b = 1

Thus, a = 8

Number is 18.