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:
$25\%$
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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