Question : A shopkeeper sells rice at 10% profit and uses a weight that is 30% less than the actual measure. His gain percentage is:
Option 1: $57\frac{1}{8}\%$
Option 2: $57\frac{1}{7}\%$
Option 3: $57\frac{2}{5}\%$
Option 4: $57\frac{3}{7}\%$
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Correct Answer: $57\frac{1}{7}\%$
Solution : Let the cost price (CP) of 1 kg. of rice be Rs. 100. As he uses 30% less weight and sells at 10% profit, Selling price (SP) of (1000 – 300) = 700 gm of rice = Rs. 110 ⇒ SP of 1000 gm of rice = $\frac{110}{700}×1000$ = $\frac{1100}{7}$ So, profit = SP – CP = $\frac{1100}{7}-100$ = $\frac{400}{7}$ Profit Percentage = $\frac{\text{Profit}}{\text{CP}}×100$ = $\frac{\frac{400}{7}}{100}×100$ = $\frac{400}{7}$ = $57\frac{1}{7}\%$ Hence, the correct answer is $57\frac{1}{7}\%$.
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