Q. In a factory, the percentage of male workers was $53.7802\%$ (rounding to nearest fourth decimal place) last year. What is the smallest number of female workers working there? Hint: Diophantine Approximation
a. $1381$
b. $593$
c. $690$
d. $440$
So I know $46.21979\%$ of the workers are female. By trial and error I found that $593/1283 = 0.4621979$. And it checks out that $(1283-593) = 690$ and $690/1283$ is $0.537802$. Which seems correct.
However my question is that, is there a better way to do this question? If I didn't have the list of options, it would've been almost impossible to do it by trial and error.