How old is the man?

The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife. How old is the man?

Let M be the age of the man and W be the age of his wife.

Given sum of their ages is 99 => M+W = 99 ----(1)
Also the man is 9 years older than his wife => M = W+9 ---(2)
i.e; M-W=9 ----(3)

Adding (1) and (3)
2M = 99+9 = 108
M = 54
W = 54-9 = 45

The man is 54 years old.