The sum of the digits of a 2-digit number is 8. If we add 36 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, $$x + y = 8$$ --------------(i)

According to question, => $$10x + y + 36 = 10y + x$$

=> $$9y - 9x = 36$$

=> $$y - x = \frac{36}{9} = 4$$ --------------(ii)

Adding equations (i) and (ii), we get :

=> $$(y+y)=(8+4)$$

=> $$y = \frac{12}{2}=6$$

Substituting it in equation (i), => $$x=8-6=2$$

$$\therefore$$ Number = 26

=> Ans - (A)