Shakuntala says, "If you reverse my age, it displays my husband's age in reverse. Indeed, he is older than me in age, and the difference in our ages is 1/11th of the product of our ages." Find out Shakuntala's age. Option 1) 23 years Option 2) 34 years Option 3) 45 years Option 4) None of these

Shakuntala says, "If you reverse my age, it displays my husband's age in reverse. Indeed, he is older than me in age, and the difference in our ages is 1/11th of the product of our ages." Find out Shakuntala's age.

Option 1) 23 years

Option 2) 34 years

Option 3) 45 years

Option 4) None of these

The correct option is C:
45 years

Explanation:

Let's denote the digits of Shakuntala's age by $x$ (tens place) and $y$ (units place). Thus, Shakuntala's age can be expressed as $10x + y$ years. Conversely, her husband's age can be written as $10y + x$ years.

Given that the difference in their ages is $\frac{1}{11}$ of the product of their ages, we start by formulating and simplifying the given problem:

[ \begin{align*} \text{Age Difference} &= |(10y + x) - (10x + y)| = (10y + x + 10x + y) / 11 \ |9y - 9x| &= 11(x + y) \ 9y - 9x &= 11(y + x) \ 9y - 9x &= x + y \ 10x &= 8y \ \end{align*} ]

From the equation $10x = 8y$, we derive $x = \frac{4y}{5}$, implying that $x$ must be a whole number. Therefore, $y$ should be a number that, when multiplied by 4, gives a product divisible by 5.

Given $y$ as a single digit, the value that satisfies this condition is $y = 5$. Consequently, $x = 4$.

Therefore, Shakuntala's age is:

[ \text{Shakuntala's age} = 10x + y = 10(4) + 5 = 45 \text{ years} ]

Thus, the correct answer is Option C: 45 years.