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 ?
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
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