Question

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

Answer 1

let age of wife= x ears
age of man-- x + 9 years
ATQ
.......x+x+9 =99
2x=90
x= 45
x=45 ie..... 45 years
so age of wife is 45 and man's age is 45+9=54 years.....

☝☝

Answer 2

let the age of the man be XY years
man's age = 10x + y
wife's age = 10y+x
1st case-

10x+y+10y+x = 99
11x+11y = 99
11(x+y) = 99
x+y = 9-(1)

2nd case-

10x+y = 9+10y +x
10x-x+y-9y = 9
9x-9y =9- (2)
multiplying (1) by 9 
9x+9y=81-(3)
adding (2) and (3)
9x+9y +9x-9y = 81+9
18x = 90
x = 5-(4)
putting (4) in (2)
9(5)-9y = 9
45-9y = 9
-9y = -36
y = 4

therefore man's age = 54 
             & wife's age = 45