a trader has 50 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. on the whole his loss is 4% . what is the quantity sold at 14% profit and that at 6% loss?

A trader has 80 kg of rice, part of which he sells at 15% profit and the rest at 5% loss, resulting in an overall gain of 12%. To find the quantity sold at 15% profit, we use the allegation method:

• The ratio of quantities sold at 15% profit to 5% loss is 17:3.
• Therefore, the quantity sold at 15% profit is 80×1717+3=6880\times \frac{17}{17+3}=6880×17+317​=68 kg

In another example, a trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. The profit percentage in this transaction is calculated as follows:

• Total cost price = 26×20+30×36=160026\times 20+30\times 36=160026×20+30×36=1600 Rs.
• Total selling price = (26+30)×30=1680(26+30)\times 30=1680(26+30)×30=1680 Rs.
• Profit = 1680 - 1600 = 80 Rs.
• Profit percentage = 801600×100=5%\frac{80}{1600}\times 100=5%160080​×100=5%

Thus, depending on the scenario, the trader's profit or loss calculations involve mixing quantities sold at different profit/loss rates and using weighted averages or allegation methods to find quantities or profit percentages.