Question : What is the profit percentage of a dishonest cloth merchant who uses a scale which measures $16 \frac{2}{3} \%$ less than what is marked on it, and also sells at a price 10% higher than the cost price?
Option 1: 20%
Option 2: 32%
Option 3: 26%
Option 4: 30%
Correct Answer: 32%
Solution :
Profit percentage = $\frac{\text{Selling price}-\text{Cost price}}{\text{Cost price}}\times100$
Let the cost price for 100 parts of a cloth be Rs. 100.
Then, the actual cost price for the merchant for cloth is 100 - 16.67 = Rs. 83.33
Since he sells at a price 10% higher than the cost price, the selling price is Rs. 110
Profit percentage = $\frac{110-83.33}{\text{83.33}}\times100 $ = 32%
$\therefore$ The profit percentage of the merchant is 32%
Hence, the correct answer is 32%.
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