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 ?

Solution(By Examveda Team)

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