THEIR AGES.

"My husband's age," remarked a lady the other day, "is represented by
the figures of my own age reversed. He is my senior, and the difference
between our ages is one-eleventh of their sum."

Husband age = 54
Wife age= 45
Difference between their ages = (1/11) * (54+45) = (1/11) * (99) = 9
Which is, 54-45 = 9

Husband age = 54
Wife age= 45
Difference between their ages = (1/11) * (54+45) = (1/11) * (99) = 9
Which is, 54-45 = 9

I want to know the equation

i want to know the equation

I haven't used any equation for this. I'll tell how I did it.
Take any 2 numbers so that after reversing them, the difference between them shouldn't be too much, as the difference in the ages of wife and husband will increase.
so, numbers that will come to you would be like this,
23 and 32, 34 and 43 etc.
If you notice, the difference in all the cases will be 9.
As per the clause given by wife, the difference in their ages is equal to 1/11th of the sum of their ages.
therefore, wife's age = a, husband's age = b, so b - a =9
b - a = (1/11) * (a + b),
9 = (1/11) * (a + b),
a + b = 99
and, b - a = 9,
On solving, we get a = 45, and b = 54

I haven't used any equation for this. I'll tell how I did it.
If you notice, the difference in all the cases will be 9.
As per the clause given by wife, the difference in their ages is equal to 1/11th of the sum of their ages.
therefore, wife's age = a, husband's age = b, so b - a =9
b - a = (1/11) * (a + b),
9 = (1/11) * (a + b),
a + b = 99
and, b - a = 9,
On solving, we get a = 45, and b = 54

Rest I got, If you notice, the difference in all the cases will be 9. , this was the biggest clue I was missing... gr8