Let the digits at tens place and ones place: \\\\(x\\\\) and \\\\(9 - x\\\\) respectively.\\\\(\ herefore\\\\) original number \\\\(= 10 x + (9 - x)\\\\)\\\\(= 9x + 9\\\\)Now Interchange the digits: Digit at ones place and tens place: \\\\(x\\\\) and \\\\(9 - x\\\\) respectively.\\\\(\ herefore\\\\) New number: \\\\(10 (9 - x) + x\\\\)\\\\(= 90 - 10x + x\\\\)\\\\(= 90 - 9x\\\\)AS per the questionNew number \\\\(=\\\\) Original number \\\\(+ 27\\\\)\\\\(90 - 9x = 9x + 9 + 27\\\\)\\\\(90 - 9x = 9x + 36\\\\)\\\\(18x = 54\\\\)\\\\(x = \\dfrac {54}{18}\\\\)\\\\(x = 3\\\\)Digit at tens place \\\\(\\Rightarrow 3\\\\) and one's place : \\\\(6\\\\)\\\\(\ herefore\\\\) Two digit number: \\\\(36\\\\)