If the two digits of the age of Mr. Manoj are | vedclass

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(D) Let the age of Mr. Manoj be $(10x + y)$ years.Then,his wife's age is $(10y + x)$ years.According to the problem,$\frac{1}{11}$ of the sum of their

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$9 	ext{ years}$

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(D) Let the age of Mr. Manoj be $(10x + y)$ years.Then,his wife's age is $(10y + x)$ years.According to the problem,$\frac{1}{11}$ of the sum of their ages is equal to the difference between their ages:$\frac{1}{11} (10x + y + 10y + x) = (10x + y) - (10y + x)$$\frac{1}{11} (11x + 11y) = 9x - 9y$$x + y = 9(x - y)$$x + y = 9x - 9y$$10y = 8x$$\frac{x}{y} = \frac{10}{8} = \frac{5}{4}$Since $x$ and $y$ are single digits,we take $x = 5$ and $y = 4$.Therefore,Mr. Manoj's age is $54$ years and his wife's age is $45$ years.The difference between their ages is $54 - 45 = 9$ years.

If the two digits of the age of Mr. Manoj are reversed,then the new age so obtained is the age of his wife. $\frac{1}{11}$ of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is older than his wife,then find the difference between their ages.

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