The sum of digits of a two-digit number is 9. When the digits are reversed, the number decreases by 45. Find the number. A. 45 B. 72 C. 63 D. 27

Let the number be 10a + b with a + b = 9. Reversing the digits decreases it by 45: (10a + b) − (10b + a) = 9(a − b) = 45, so a − b = 5. With a + b = 9, a = 7 and b = 2, so the number is 72 (reversed it becomes 27, which is 45 less).