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
বিকল্পসমূহ (নিজের উত্তর যাচাই করতে ক্লিক করুন):
সঠিক উত্তর
2 (45 years)
বিস্তারিত ব্যাখ্যা ও বিশ্লেষণ:
Solution:
Let x and y be the ten's and unit's digits of the woman's age, respectively.
Then, Woman's age = 10x + y years
Husband's age = 10y + x years
According to the question:
(10y + x) − (10x + y) = (1/11) × (10y + x + 10x + y)
⇒ 9y − 9x = (1/11)(11y + 11x)
⇒ 9(y − x) = x + y
⇒ 9y − 9x = x + y
⇒ 10x = 8y
⇒ x = (4/5)y
Since y is a single-digit and must make x a whole number, the only valid value for y is 5.
⇒ x = 4
Therefore: Woman's age = 10×4 + 5 = 45 years
