A stockist wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit?

### Concept & Comparative Profit Scenarios To compare different profit-making strategies, calculate the profit percentage for each method by strictly identifying the actual Cost Price (value of goods actually given) and the Selling Price (money received). ### Step-by-Step Solution Let the standard CP of $1000$g ($1$ kg) of sugar be Rs. $1000$ (Re. $1$ per gram). * **Method (a): Sell sugar at $10\%$ profit** * SP = Rs. $1100$, CP = Rs. $1000$. * Profit = $10\%$. * **Method (b): Use $900$ g of weight instead of $1$ kg** * He gives $900$g (Actual CP = Rs. $900$) and charges for $1000$g (SP = Rs. $1000$). * Profit = $1000 - 900 = 100$. * Profit % = $\frac{100}{900} \times 100 = \frac{100}{9}\% \approx 11.11\%$. * **Method (c): Mix $10\%$ impurities in sugar and sell at cost price** * He has $1000$g sugar and adds $100$g free impurities, making an $1100$g mixture. * He sells the $1100$g at the CP rate of pure sugar (Re. $1$/gram). Total SP = Rs. $1100$. * His actual cost is only for the $1000$g pure sugar. Actual CP = Rs. $1000$. * Profit = $1100 - 1000 = 100$. * Profit % = $\frac{100}{1000} \times 100 = 10\%$. * **Method (d): Increase the price by $5\%$ and reduce the weight by $5\%$** * He charges $5\%$ more for $1$ kg. SP = $1000 + 5\% = \text{Rs. } 1050$. * He gives $5\%$ less weight. Actual weight = $950$g. Actual CP = Rs. $950$. * Profit = $1050 - 950 = 100$. * Profit % = $\frac{100}{950} \times 100 = \frac{1000}{95} = \frac{200}{19}\% \approx 10.52\%$. Comparing the percentages: $10\%$, $11.11\%$, $10\%$, and $10.52\%$. The highest is $11.11\%$. ### Exam Strategy & Shortcut You can evaluate these rapidly using fractions: (a) Profit fraction = $1/10$ (b) Profit fraction = $\frac{1000-900}{900} = 1/9$ (c) Profit fraction = $100/1000 = 1/10$ (d) Profit fraction = $\frac{105 - 95}{95} = 10/95 = 2/19$ Comparing $1/10$, $1/9$, and $2/19$: $1/9$ ($0.111$) is larger than $1/10$ ($0.10$) and $2/19$ ($\approx 0.105$). ### Common Pitfall A common misjudgment in option (c) is calculating profit over $1100$g instead of the $1000$g cost base, or assuming mixing $10\%$ impurities yields more than $10\%$ profit. Always ground the denominator in the actual cost out of pocket. ### Final Answer Therefore, the correct answer is **Use $900$ g of weight instead of $1$ kg**.