Explanation:

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10x + y) years; husband's age = (10y + x) years.

Therefore (10y + x) - (10x + y) = (1/11) (10y + x + 10x + y)

(9y - 9x) = (1/11)(11y + 11x) = (x + y)   =>  10x = 8y   =>  x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x = 4, y = 5.

Hence, woman's age = 10x + y = 45 years