2018 · Q39
The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages?
Elementary MathematicsNumber System
- A8 years
- B9 years
- C10 years
- D11 years
Explanation
Let the ages be 10a + b and 10b + a with b > a. The difference 9(b − a) equals one-eleventh of the sum 11(a + b), i.e. a + b. Then 9(b − a) = a + b gives 8b = 10a, so (a, b) = (4, 5): ages 45 and 54, differing by 9 years, option (B).