The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

A. 49
B. 94
C. 83
D. Either (a) or (b)
E. None of these

Explanation:

Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 — (1)
10b + a = 10a + b – 45
45 = 9a – 9b => a – b = 5 — (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.