Question

the age of a man is 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?

Answer 1

Let the digits of age of the wife be 10x + y

(While writing two digits number, it's format is 10a + b)

So reverse = 10y + x

Given that, reverse of wife's age = man's age

=> Man's age = 10y + x

Also given that,

Wife's age + 9 = man's age

10x + y + 9 = 10y + x

=> 9 = 10y + x - 10x - y

=> 9 = 9y - 9x

=> 9y - 9x = 9

=> 9(y - x) = 9

=> y - x = 9/9

=> y - x = 1 .......... equation (1)

Also given that,
Wife's age + man's age = 99

=> 10x + y + 10y + x = 99
=> 11x + 11y = 99

=> 11(x + y) = 99

=> x + y = 99/11

=> x + y = 9 .......(equation 2)

Adding equation 1 and equation 2, we get

y - x + x + y = 1 + 9

=> 2y = 10

=> y = 10/2

=> y = 5

Putting the value of y in equation 1

y - x = 1

=> 5 - x = 1

=> -x = 1 - 5

=> -x = -4

=> x = 4

Now age of wife = 10x + y

=> 10(4) + 5

=> 40 + 5

=> 45

And age of man is reverse

=> 54


So age of man = 54
age of wife = 45


Hope it helps dear friend ☺️✌️
Nice question!

Answer 2

Here is your solution

Given that :-

The age of a man is same as his wife

age with the digits reversed then sum of their ages is 99 and the man is 9 years order than his wife


Let
The man age = 10x +y

wife age = 10y +x

sum of the ages = 99

10x+y +10y +x =99

11x +11y =99

x+y =9................................................ (1)

man age = wife age+9

10x +y = 10y +x+9
10x-x +y -10y =9
9x -9y =9


x-y =1 ...............................................(2)

Adding equation (1) and (2)

2x =10
x= 10/2
x= 5

putting the value of x=5 in equation (1)

y= 4

Hence,
man age =10x+y = 10*5 +4 =50+4 = 54✔

Age of wife = 45 years. ✔

Hope it helps you