A dishonest dealer sells the goods at $20\%$ loss on cost price but uses $15\%$ less weight. What is his percentage profit or loss?

### Concept & Net Profit/Loss with False Weights Even if a dealer sells at a loss based on price, giving less weight can offset the loss. The net outcome depends on comparing the actual cost of the goods given with the money received. ### Step-by-Step Solution * Let the cost price of $100$g of goods be Rs. $100$. * The dealer sells at a $20\%$ loss. * Selling Price (SP) for a promised $100$g = $100 - 20 = \text{Rs. } 80$. * He uses $15\%$ less weight. So, for a promised $100$g, he actually delivers $100 - 15 = 85$g. * The actual Cost Price (CP) for the dealer is the cost of the $85$g given, which is Rs. $85$. * Now, we compare the actual CP (Rs. $85$) to the SP (Rs. $80$). * Since SP < CP, there is a loss. * Loss amount = $85 - 80 = \text{Rs. } 5$. * Loss percentage = $\frac{\text{Loss}}{\text{Actual CP}} \times 100 = \frac{5}{85} \times 100$. * Simplify the fraction: $\frac{5}{85} = \frac{1}{17}$. * Loss percentage = $\frac{100}{17}\% = 5 \frac{15}{17}\%$ loss. ### Exam Strategy & Shortcut Use the ratio method. Let the initial state be $100$. Due to price: Value becomes $80$. Due to weight: Cost base is actually $85$. Net ratio = $80 / 85 = 16 / 17$. Loss = $1$ part on a base of $17$. $\frac{1}{17} \times 100 = 5 \frac{15}{17}\%$ loss. ### Common Pitfall A common mistake is applying the loss percentage to the actual weight given or subtracting the percentages directly ($-20\% + 15\% = -5\%$). This ignores the different bases of the percentages. ### Final Answer Therefore, the correct answer is **$5 \frac{15}{17}\%$ loss**.