Let the number of processed eggs per day = p
Let the number of accepted eggs per day = a
Let the number of rejected eggs per day = r
a = p - r


Given that for every 96 eggs accepted for processing 4 eggs were rejected
$$a:r=96:4$$
$$\frac{p-r}{r}=\frac{96}{4}$$
$$=\frac{p-r}{r}=\frac{24}{1}$$
$$p-r=24r$$
$$p=2r+r$$
$$p=25r$$
On a particular day 12 additional eggs were accepted but overall number of eggs inspected remains the same and a + 12 : r - 12 = 99 :1
$$\frac{p-r+12}{r-12}=\frac{99}{1}$$
$$p-r+12=99\left(r-12\right)$$
$$p-r=99r-1188-12\ where\ p=25r$$
$$25r-r-99r=-1200$$
$$\frac{-75r}{-75}=\frac{-1200}{-75}$$
$$r=16$$
$$p=25\cdot16=400eggs\ \ per\ day$$
$$Answer\ =\ C$$