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1. 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 ?

A. 40

B. 100

C. 200

D. 72

Solution:

Let the total number of eggs bought be a
10% of eggs are rotten
∴ Remaining eggs :

\begin{aligned} = a - 10 % of a \\ = a - \frac{10 a}{100} \\ = \frac{100 a - 10 a}{100} \\ = \frac{90 a}{100} \\ = \frac{9 a}{10} \end{aligned}

Man gives 80% of

\frac{9 a}{100}

eggs to his neighbour

\begin{aligned} = \frac{80}{100} \times \frac{9 a}{10} \\ = \frac{72 a}{100} \end{aligned}

Remaining eggs :

\begin{aligned} = \frac{9 a}{10} - \frac{72 a}{100} \\ = \frac{90 a - 72 a}{100} \\ = \frac{18 a}{100} \\ = \frac{9 a}{50} \end{aligned}

According the question,

\begin{aligned} \Rightarrow \frac{9 a}{50} = 36 \\ \Rightarrow 9 a = 36 \times 50 \\ \Rightarrow a = \frac{36 \times 50}{9} \\ \Rightarrow a = 200 \end{aligned}

Hence, the total number of eggs bought be = 200

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