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 hi wife. how old is the man

Answer 1

let the man age = 10x +y

wife age = 10y +x
sum of the ages =99
10x+y +10y +x =99
11x +11y =99

divide each term with 11
x+y =9 ----(1)

man age = wife age+9
10x +y = 10y +x+9
10x-x +y -10y =9
9x -9y =9
divide each term with 9

x-y =1 ---(2)

add (1) and (2)
2x =10
x= 10/2
x= 5
plug x=5 in (1)

y= 4
therefore
man age =10x+y
 = 10*5 +4
=50+4
= 54

wife age = 45