A grain merchant professes to sell wheat flour at its cost price, but uses a fraudulent weight that measures only $900\text{ grams}$ for a kilogram ($1,000\text{ grams}$). What is the merchant's actual profit percentage? ________ % (round off to two decimal places).
Answer Key:
11.11
Step-by-Step Solution & Explanation
**Method 1: Standard False Weight Formula**
$\text{Profit } \% = \frac{\text{Error}}{\text{True Weight} - \text{Error}} \times 100 = \frac{1000 - 900}{900} \times 100 = \frac{100}{900} \times 100 = \frac{1}{9} \times 100 = 11.11\%$
**Method 2: Cost-Price Ratio Formulation**
Let cost price of $1\text{ g} = ext{Rs. }1$. Cost of $900\text{ g}$ sold is $ ext{Rs. }900$, while revenue obtained is $ ext{Rs. }1,000$.
$\text{Profit } \% = \frac{1000 - 900}{900} \times 100 = 11.11\%$