My friend sent me a question from an olympiad and im not sure that we have followed the right method, we both did the same thing:
The age of a man was 2/61 of the year in which he died. How old would he have been if he lived until 1992?
Surly then he dies in 1992 and then his age is 2/61 times 1992 rounded to the nearest integer? I am unsure though, this seems too simple.
If you let $a$ be the age of the man in the year in which he died and $d$ be the year of his death, then $a=\frac {2d}{61}$.
Since $61$ is prime and $a$ is an integer we have to have $d=61k$, in which case $a=2k$.
So if, for example, $k=32$ then $d=1952$ and $a=64$, which would give an age of [ ] in $1992$.
If $k=31$ then $d=1891$ and $a=62$ implying age [ ] in $1992$. To exclude this possibility (and others) you have to use a nonmathematical assumption, for example that human beings do not live beyond age $120$.