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Age puzzle with reversed digits and ratio condition: Determine the woman's present age. When the woman's age digits are reversed, the result is her husband's age. He is older than she is. The difference between their ages equals one-eleventh of their sum. Find the woman's current age. Choose the correct value.

Difficulty: Medium

Correct Answer: 45 years

Explanation:


Let ages
Woman = 10a + b, Husband = 10b + a, with b > a (husband older).


Given ratio/difference condition
Difference = (1/11) × Sum (10b + a) − (10a + b) = (1/11)[(10b + a) + (10a + b)] 9(b − a) = (1/11)·11(a + b) ⇒ 9(b − a) = a + b ⇒ 8b = 10a ⇒ 4b = 5a.


Digit solutions
Let a = 4k, b = 5k with digits 0–9 ⇒ k = 1 works: a = 4, b = 5. Woman = 10·4 + 5 = 45, Husband = 54 (older ✔).

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