Define Cost and Sale variables

Assume the true weight of 100 units has a cost of $100$. The trader sells this at a 74% profit, so the selling price is $174$.

$\text{Cost} = 100, \text{Selling Price} = 174$

Account for false weight

The trader uses a weight 9% less than intended, meaning he actually gives only 91 units of weight while charging for 100. Thus, his actual cost price for the weight sold is $91$.

$\text{Actual Cost Price} = 91$

Calculate Profit Percentage

Actual profit is the difference between Selling Price ($174) and \text{Actual} \text{Cost} ($91). Profit % = ((174 - 91) / 91) * 100.

$\text{Profit} \% = \left( \frac{83}{91} \right) \times 100 \approx 91.208\%$

Final Rounding

Rounding 91.208% to the nearest whole number gives 91%.

$91\%$