A woman says, “If you reverse my own age, the figures represent my husbands age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum.” The womans age is
23 years
34 years
45 years
None of these
Explanation:
Let x and y be the tens and units digits respectively of the numeral denoting the womans age.Then, womans age = (10X + y) years; husbands 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)yClearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, womans age = 10x + y = 45 years.
Let x and y be the tens and units digits respectively of the numeral denoting the womans age.Then, womans age = (10X + y) years; husbands 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)yClearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, womans age = 10x + y = 45 years.