The sum of the digits of a 2 digit number is 9, When 27 is added to the number, the digits get interchanged. Find the number. A. 45 B. 36 C. 18 D. 27

Let the number be 10a + b with a + b = 9. Adding 27 swaps the digits: 10a + b + 27 = 10b + a, so 9(b − a) = 27 and b − a = 3. With a + b = 9, a = 3 and b = 6, so the number is 36 (36 + 27 = 63).