The sum of the digits of a 2-digit number is 11. If we add 45 to the number, the new number obtained is a number formed by interchange of the digits. What is the number?

Let the unit's digit of the number be $$y$$ and ten's digit be $$x$$

=> Number = $$10x + y$$

Sum of digits = $$x + y = 11$$ --------------(i)

According to question, => $$10x + y + 45 = 10y + x$$

=> $$9y - 9x = 45$$

=> $$y - x = \frac{45}{9} = 5$$ --------------(ii)

Adding equations (i) and (ii), we get : $$2y = 11 + 5 = 16$$

=> $$y = \frac{16}{2} = 8$$

Substituting it in equation (i), => $$x = 11 - 8 = 3$$

$$\therefore$$ Number = 38