A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by

### Concept & Total Effective Cost When free items are given, the Cost Price for the seller includes the cost of both sold and free items, while revenue is only generated from the sold items. Calculate total cost and total revenue based on the bundle size. ### Step-by-Step Solution - Let the Cost Price (CP) of 1 article be Rs. 100. - The tradesman sells 15 articles and gives 1 free. This forms a bundle of 16 articles. - Total Cost Price for the tradesman for this bundle = $16 \times 100 = \text{Rs. } 1600$. - He gains a net profit of $35\%$ on the whole transaction. - Total Selling Price (Revenue) for the bundle = $\text{Total CP} \times 1.35 = 1600 \times 1.35 = \text{Rs. } 2160$. - This revenue comes entirely from the 15 paid articles. - Selling Price per paid article = $\frac{2160}{15} = \text{Rs. } 144$. - This SP is after a $4\%$ discount on the Marked Price (MP). - $\text{MP} \times (1 - 0.04) = 144 \Rightarrow \text{MP} \times 0.96 = 144$. - $\text{MP} = \frac{144}{0.96} = \frac{14400}{96} = 150$. - The CP is Rs. 100 and the MP is Rs. 150. - The Marked Price is $50$ above the Cost Price, which is a $50\%$ markup. ### Exam Strategy & Shortcut Using a combined formula approach: Total Cost is for 16 items. Revenue is for 15 items at discounted MP. Profit is $35\%$. $15 \times \text{MP} \times 0.96 = 16 \times \text{CP} \times 1.35$. $\frac{\text{MP}}{\text{CP}} = \frac{16 \times 1.35}{15 \times 0.96} = \frac{21.6}{14.4} = \frac{216}{144} = \frac{3}{2} = 1.5$. This means MP is $150\%$ of CP, which is a $50\%$ markup. ### Common Pitfall A frequent error is calculating the $35\%$ profit on the cost of 15 articles instead of 16. The tradesman incurs the cost for the free article as well, so total CP must reflect all items given. ### Final Answer Therefore, the correct answer is **50%**.