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The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages?

The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages? Correct Answer 9 years

Let the two digits of the age of the women be y and x (yx)

Age of the woman = 10y + x

Age of the man = 10x + y

Difference in their ages = 10x + y - 10y - x

⇒ 9x - 9y

Sum of their ages = 10x + y + 10y + x = 11x + 11y

Difference = 1/11 × Sum

9x - 9y = 1/11 × (11x + 11y)

9x - 9y = x + y

8x = 10y

Since x and y can only be natural numbers from 1 to 9, the only possibility is x = 5 and y = 4

Difference in their age = 9x - 9y = 45 - 36 = 9 years

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