Recently I met a women which said: Do you know something funny? If you reverse my own age, the figures represent my husbands age. He is, of course, senior to me, and the difference between our age is $\frac{1}{11}$ of their sum.

Can you find out the women's age as well as her husband's age?


Their ages are:

Wife: $45$, Husband: $54$


Let wife's age be represented as: $10x+y$ where $x$ and $y$ are single digit natural numbers. Now, husband's age is $10y+x$. So, now, difference of their ages: $9y-9x = \frac{1}{11}(11x+11y) = x+y = k$. So, $9x+9y=9k$ and $9y-9x = k$. Thus, $y=\frac{5k}{9}, x=\frac{4k}{9}$. So, since $x, y$ are digits and are strictly integers, the only possible answer is $k=9$. Thus leading us to the answer.

  • $\begingroup$ In fact, it is not mention in the problem that the ages are two-digit numbers. Other answers include $495, 4995, 49995, \dots$ and there are even more, such as $4545$ and $495495$. It is easy to show that any answer must begin with $4$ and end with $5$. $\endgroup$ – WhatsUp Aug 18 '20 at 2:06
  • $\begingroup$ And actually it is this OEIS sequence. $\endgroup$ – WhatsUp Aug 18 '20 at 2:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.