A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and difference between our ages is one-eleventh of their sum". The woman's age is _____?
- 34 years
- 45 years
- 23 years
- None of these
Explanation
Let's assume the woman's age is represented as 10a + b.
Reversing the digits, her husband's age would be 10b + a.
Given that the husband is senior to her:
10b + a > 10a + b
9b > 9a
b > a
The difference between their ages is:
(10b + a) - (10a + b) = 9b - 9a
The sum of their ages is:
(10b + a) + (10a + b) = 11b + 11a
Given that the difference is one-eleventh of the sum:
9b - 9a = (1/11)(11b + 11a)
9b - 9a = b + a
8b = 10a
4b = 5a
Since a and b are single-digit integers, the possible solution is a = 4 and b = 5.
Woman's age: 10a + b = 10(4) + 5 = 45
Husband's age: 10b + a = 10(5) + 4 = 54
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