Let, $X$ be the expected number of children a parent has.
So, expected number of boys $= 1$ and expected number of girls $= X - 1.$
The probability of having a baby boy $= 0.51.$
And the probability of having a baby girl $= 0.49.$
So,
$X = 1 \times (0.51) + 2 \times (0.49) \times (0.51) + 3 \times (0.49)^2 \times (0.51) + 4 \times (0.49)^3 \times (0.51) $
$0.49X= 1 \times (0.49) \times (0.51) + 2 \times (0.49)^2 \times (0.51) + 3 \times (0.49)^3 \times (0.51) $
$X - 0.49X = (0.51)[ 1 + (0.49) \times (0.51) + (0.49)^2 \times (0.51) + (0.49)^3 \times (0.51) + \ldots ]$
$0.51X = (0.51) [ 1 / 0.51 ]$
$\implies X = 100 / 51.$
So, No of girl children $= X - 1.$
$\quad \quad = [100 / 51 ] - 1 = 49 / 51.$
No. of boy children $= 1.$
Hence, Ratio of Boys and Girls $= 51 : 49.$
[ Ans - A ]