Question : A dealer sold $\frac{3}{4}$th of his articles at a gain of $24\%$ and the remaining at the cost price. The percentage of gain in the whole transaction is:
Option 1: $15\%$
Option 2:
$18\%$
Option 3:
$24\%$
Option 4:
$32\%$
Correct Answer:
$18\%$
Solution :
Let the cost price of each article be $\mathrm{C}$.
The dealer sold $\frac{3}{4}$th of his articles at a gain of $24\%$.
The selling price for this part $=\mathrm{\frac{3}{4}C + 0.24 \times \frac{3}{4}C = 0.93C}$
The remaining $\frac{1}{4}$th of the articles were sold at the cost price.
The selling price for this part $=\mathrm{\frac{1}{4}C}$
The total selling price $=\mathrm{0.93C + 0.25C = 1.18C}$
The percentage of gain $=\mathrm{\frac{1.18C-C}{C}×100=18\%}$
Hence, the correct answer is $18\%$.
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