A woman says, ''if you reverse my own age, the figure represents my husband's age. He is, of course, senior to me and the difference between our ages is one eleventh of our sum. ''What is the age of the woman?
Solution
Correct Answer: Option 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;
So, husband's age = (10y + x) years.
Therefore (10y + x) - (10X + y) = (1/11) (10y + x + 10x + y)
⇒ (9y - 9x) = (1/11)(11y + 11x) = (x + y)
⇒ 10x = 8y
⇒ 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.
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