I think the answer should be b.
The way I did it is that say we take the total number of eggs to be x. Then, we can consider all the options and check the expected loss.
For option a, the expected loss will be x/2.
For b, it will be x/5.
For c, it will be x/4+x/10=7x/20>x/5.
For d, it will be 3x/8+x/20=17x/40>x/5.