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
Answer: C
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 \((10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)\)
\(\Rightarrow\) (9y-9x) = (1/11)(11y + 11x) = (x + y)
\(\Rightarrow\) \(10x = 8y\)
\(\Rightarrow\) \( x = (4/5)y\)
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