Vijay buys some eggs. After bringing the eggs home, he finds two to be rotten and throws them away. Of the remaining eggs, he puts five-ninth in his fridge , and brings the rest to his mother, Rashmi's house. She cooks two eggs and puts the rest in her fridge. If her fridge cannot hold more than five eggs, what is the maximum possible number of eggs bought by Vijay ?

Let the eggs bought by Vijay be N.
Vijay throws 2 eggs, so remaining=N-2
Eggs in Vijay's fridge=$$\frac{5}{9}\left(N-2\right)$$
Remaining eggs=$$\frac{4}{9}\left(N-2\right)$$
Rashmi cooks 2 eggs, so Eggs in her fridge = $$\frac{4}{9}\left(N-2\right)\ -\ 2$$
$$\frac{4}{9}\left(N-2\ \right)-\ 2\ \le\ 5$$
N$$\le$$17.75
Also, for $$\ \frac{5}{9}\left(N-2\right)$$ and $$\ \frac{4}{9}\left(N-2\right)$$ to be an integer N-2=9k (k is an integer greater than 0)
N=9k+2=11,20,....
Maximum possible value of N is 11.
Option A is the answer.