Question

A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is

• A. $23$ years
• B. $34$ years
• C. $45$ years
• D. None of these

Answer 1

The correct option is C $45$ years

Let $x$ and $y$ be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age $=(10x+y)$ years; husband's age $=(10y+x)$ years.
Therefore $(10y+x)-(10x+y)=\left(1/11\right)(10y+x+10x+y)$
$\iff (9y-9x)=\left(1/11\right)(11y+11x)=(x+y)\iff 10x=8y\iff x=\left(4/5\right)y$
Clearly, $y$ should be a single-digit multiple of $5$, which is $5$.
So, $x=4$, $y=5$.
Hence, woman's age $=10x+y=45$ years.