The sum of the digits of a 2-digit number is 17. If we add 9 to the number, the new number obtained is a number formed by interchange of the digits. Find the number.

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

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

Sum of digits = $$x + y = 17$$ --------------(i)

According to question, => $$10x + y + 9 = 10y + x$$

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

=> $$y - x = \frac{9}{9} = 1$$ --------------(ii)

Adding equations (i) and (ii), we get : $$2y = 17 + 1 = 18$$

=> $$y = \frac{18}{2} = 9$$

Substituting it in equation (i), => $$x = 17 - 9 = 8$$

$$\therefore$$ Number = 89

=> Ans - (A)