Reverse a wife's age to get her husband's; their gap is 1/11 of the total
A husband is older than his wife, and his age in years is exactly her age written with the two digits swapped. The difference between their ages is exactly one-eleventh of their combined ages. How old is each of them?
Reveal the answer
The wife is 45 and the husband is 54. Writing her age with digits a and b, his is the same digits reversed; the gap between a two-digit number and its reversal is always 9 times the difference of its digits, and setting that gap equal to 1/11 of their 99-year combined total forces the digits to 4 and 5, giving 45 and 54, a 9-year gap. This is Puzzle No. 41, 'Their Ages,' from Henry Dudeney's 1917 Amusements in Mathematics.
— Henry Ernest Dudeney, Amusements in Mathematics — Puzzle No. 41, 1917