Akram is older than his wife. If the digits of his wife’s are reversed, it will represent the Akram's age. The difference between their ages is 1/11 of their sum, the woman’s age is?

22 years

45 years

34 years

None of these

Let's denote Akram's age as 10a + b and his wife's age as 10b + a, where a > b.

Given the difference between their ages is 1/11 of their sum:

(10a + b) - (10b + a) = 1/11 * ((10a + b) + (10b + a))

9a - 9b = 1/11 * (11a + 11b)

9(a - b) = a + b

9a - 9b = a + b

8a = 10b

4a = 5b

Possible values for (a, b) given a > b:

(5, 4)

Akram's age: 10_5 + 4 = 54

Wife's age: 10_4 + 5 = 45