Puneet buys 240 articles and labels each with the same marked price. He sells 160 articles initially at 20% discount on the labelled price. Then he sells rest articles at an additional discount of 25% on the discounted price. Thus, he gets total of ₹Z, and makes profit of 10%. When he offered no discount find its profit %.

### Concept & Profit Calculation The core concept involves relating Cost Price (CP), Selling Price (SP), and Marked Price (MP). Profit percentage is always calculated on the base Cost Price: $$ \text{Profit } \% = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 $$ ### Step-by-Step Solution * Let the Cost Price (CP) of 1 article be $1$ unit. Total CP for 240 articles = $240$. * Let the Marked Price (MP) of each article be $M$. * The total Selling Price (SP) is ₹Z. Since there is an overall profit of 10%, the total SP must be $110\%$ of the total CP: $\text{Total SP} = 240 \times 1.10 = 264$ units. * Now, let's calculate the SP based on the discounts: * First 160 articles are sold at a 20% discount on MP. $\text{SP}_1 = 160 \times (M \times (1 - 0.20)) = 160 \times 0.8M = 128M$ * The remaining 80 articles are sold at an *additional* 25% discount on the *already discounted* price ($0.8M$). $\text{New Discounted Price} = 0.8M \times (1 - 0.25) = 0.8M \times 0.75 = 0.6M$ $\text{SP}_2 = 80 \times 0.6M = 48M$ * Total SP in terms of M = $128M + 48M = 176M$. * Equate the two total SP values: $176M = 264$ $M = \frac{264}{176} = 1.5$ units. * The Marked Price (MP) is $1.5$ per article, while the Cost Price (CP) is $1$ per article. * If no discount is offered, the new SP equals the MP ($1.5$). * Profit = $1.5 - 1 = 0.5$. * Profit % = $(\frac{0.5}{1}) \times 100\% = 50\%$. ### Exam Strategy & Shortcut Assume the CP of one article is 100 to avoid decimals. Total CP = 24000. Total SP = 26400 (10% profit). Equating the sales: $(160 \times 80\% \times M) + (80 \times 60\% \times M) = 26400 \implies 128M + 48M = 26400 \implies 176M = 26400 \implies M = 150$. If CP is 100 and MP is 150, the profit percentage without discount is simply 50%. ### Common Pitfall A common error is applying the second 25% discount to the original marked price rather than the already discounted price (successive discount). "Additional discount on the discounted price" means it compounds on the 80% value, becoming 60% overall. ### Final Answer Therefore, the correct answer is **50%**.