Question

The age of a man is same as his wife age with digits are reversed the sum of the ages is 99 the man is 9 years older than his wife

Answer 1

Answer:

Step-by-step explanation:

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

Lets take the age of man as X
Age of wife = X - 9
Sum of there reverse ages = 99
Reverse Age of man + reverse age of wife = 99
X + X - 9= 99
2X - 9 = 99
2X = 99 - 9
2X = 90
X = 90 / 2
X = 45
Reverse age of man = 45
Age of wife = X - 9
= 45 - 9
=54
Real age of man = 54
Real age of women = 45