Ratio of Boys and Girls In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)

If every family continues having children until they have one boy, then every family will have one boy; except those who haven't stopped having children yet, or those that are not able to continue due to various circumstances.   Let's ignore these, as we don't have enough information to consider such.   (Likewise how many births are twin boys?)
The expected number of girls in families which have a boy is $1$, by reason that this count a geometrically distributed random variable (of failures before success), and for $\;G\sim\mathcal{Geo_0}(p)\;$, then $\;\mathsf E(G) = (1-p)/p\;$.  
This leads to a theoretical expected ratio of $1:1$ boys to girls in the country.
Of course, we will actually expect the ratio to be somewhat higher, because there are families which have no boys (yet).   But we can't say what proportion of families these may be.
