The sum of digits of a two-digit number is 12. When the digits are interchanged, the resulting number is 36 more than the original number. What is the original two-digit number ?

Explanation

Let the original number = $$10x + y$$ => $$x + y = 12$$ On interchanging the digits, the number = $$10y + x$$ => $$(10y + x) - (10x + y) = 36$$ => $$9y - 9x = 36$$ => $$y - x = 4$$ On solving above equations, we get : => $$x = 4$$ and $$y = 8$$ $$\therefore$$ Original number = 48