Question : A shopkeeper sold $\frac{1}{3}$th of his goods at a loss of $15\%$. To get a profit of $10\%$ on the whole transaction, he should sell the remaining articles at a profit of:
Option 1: $22\frac{1}{2}\%$
Option 2:
$16\frac{2}{3}\%$
Option 3:
$15\%$
Option 4:
$25\%$
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Correct Answer: $22\frac{1}{2}\%$
Solution : The shopkeeper initially had goods worth $\mathrm{C}$. He sold $\frac{1}{3}$th of his goods at a loss of $15\%$. The selling price for this part $=\mathrm{\frac{1}{3}C - 0.15 \times \frac{1}{3}C = 0.2833C}$ To get a profit of $10\%$ on the whole transaction. The total selling price $=\mathrm{1.1C}$ The selling price for the remaining $\frac{2}{3}$th of the goods $=\mathrm{1.1C - 0.2833C = 0.8167C}$ The cost price for the remaining $\frac{2}{3}$th of the goods $=\mathrm{\frac{2}{3}C}$ The profit percentage for the remaining goods $=\mathrm{\frac{0.8167C - \frac{2}{3}C}{\frac{2}{3}C} \times 100 = 22\frac{1}{2}\%}$ Hence, the correct answer is $22\frac{1}{2}\%$.
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