A grocer sells rice at a profit of $10\%$ and uses weights which are $20\%$ less than the market weight. The total gain earned by him will be

### Concept & Successive Profit When a merchant alters both the price mark-up and the given weight, the overall profit is a combination of the price gain and the weight cheated. The actual cost price depends on the weight given, while the selling price depends on the marked up price of the promised weight. ### Step-by-Step Solution * Let the cost price of $1000$g of rice be Rs. $1000$. * The grocer promises to sell at a $10\%$ profit. * Selling Price (SP) for the promised $1000$g = $1000 + 10\%$ of $1000 = \text{Rs. } 1100$. * He uses weights that are $20\%$ less. So, for a promised $1000$g, he actually gives $1000 - 20\% = 800$g. * The actual Cost Price (CP) incurred by the grocer for this transaction is the cost of $800$g, which is Rs. $800$. * Profit = $\text{SP} - \text{Actual CP} = 1100 - 800 = 300$. * Profit percentage = $\frac{\text{Profit}}{\text{Actual CP}} \times 100 = \frac{300}{800} \times 100 = 37.5\%$. ### Exam Strategy & Shortcut Use the combined formula or ratio method: Multiplier for price = $1.10$ (due to $10\%$ profit) Multiplier for weight = $1 / 0.80$ (since he gives $80\%$ weight but gets $100\%$ payment) Overall multiplier = $1.10 \times \left(\frac{1}{0.80}\right) = \frac{1.10}{0.80} = 1.375$. This translates to a $37.5\%$ profit. ### Common Pitfall A frequent error is calculating the percentage on the promised weight (CP of $1000$) instead of the actual weight delivered (CP of $800$). Always base profit percentage on the actual goods transferred. ### Final Answer Therefore, the correct answer is **$37.5\%$**.