A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbours. Now he is left out with 36 eggs. How many eggs he bought ?

Answer: Option C

Let the total number of eggs bought be a
10% of eggs are rotten
∴ Remaining eggs :
$$\begin{array}{rl}& =a-10\%\text{ of }a\\ & =a-\frac{10a}{100}\\ & =\frac{100a-10a}{100}\\ & =\frac{90a}{100}\\ & =\frac{9a}{10}\end{array}$$
Man gives 80% of $$\frac{9a}{100}$$ eggs to his neighbour
$$\begin{array}{rl}& =\frac{80}{100}\times \frac{9a}{10}\\ & =\frac{72a}{100}\end{array}$$
Remaining eggs :
$$\begin{array}{rl}& =\frac{9a}{10}-\frac{72a}{100}\\ & =\frac{90a-72a}{100}\\ & =\frac{18a}{100}\\ & =\frac{9a}{50}\end{array}$$
According the question,
$$\begin{array}{rl}& \Rightarrow \frac{9a}{50}=36\\ & \Rightarrow 9a=36\times 50\\ & \Rightarrow a=\frac{36\times 50}{9}\\ & \Rightarrow a=200\end{array}$$
Hence, the total number of eggs bought be = 200