A shopkeeper has a certain number of eggs of which 5\% are found to be broken. He sells 93\% of the remainder and still has 266 eggs left. How many eggs did he originally have?
(a)3800
(b)4000
(c)4200
(d)None of these
Answer
Answer (as printed): B
Explanation
Let the total number of eggs originally be $x$. Then, number of eggs which are intact $=(100-5) \%$ of $x$ $$=\frac{95 x}{100}=\frac{19 x}{20} .$$ Number of eggs left unsold $=(100-93) \%$ of $\frac{19 x}{20}$ $$=\left(\frac{7}{100} \times \frac{19 x}{20}\right) . \therefore \frac{7}{100} \times \frac{19 x}{20}=266 \Rightarrow x=\left(\frac{266 \times 100 \times 20}{7 \times 19}\right)=4000 .$$
Explanation as extracted from the printed page; notation may be imperfect.