What is Probability of having a boy

In a country where everyone wants a boy(A country like India), each family continues having babies till they have a boy.
After some time, what is the proportion of boys to girls in the country? 
Note that probability of having a boy or a girl is same.

Answer:-

Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method.

Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + …
Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + …
Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + …
Number of girls = C

(using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms)

The proportion of boys to girls is 1 : 1.

Another Explanation -

Let us take an example that in a country there are 40 couples and considering same probability of a girl and a boy 25 of them will have a boy as their first child.
Here B = 20 G = 20      (B = No.of Boys, G = No. of Girls)

Now for the rest of 20 couples 10 of them will have a Boy as their second child and rest 10 will have girl again as their second child.
So here B = 30(20 + 10)
G =    30(20 + 10)

The no. of boys and girls will always be same. The answer is shocking but true.
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