Arun purchased 30 kg of wheat at the rate of ₹ 11.50 per kg and 20 kg of wheat at the rate of ₹ 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit? (Bank P.O., 2011)

### Concept & Weighted Average To find the selling price for a desired profit on a mixture, first determine the total cost of the mixture. Calculate the total cost by summing the products of individual quantities and their respective rates. $$Total\ CP = (Q_1 \times R_1) + (Q_2 \times R_2)$$ $$Required\ SP = Total\ CP \times \left(1 + \frac{Profit\ \%}{100}\right)$$ ### Step-by-Step Solution * **Total Cost Price (CP)** of the first batch (30 kg at ₹ 11.50/kg) = $30 \times 11.50 = 345$ * **Total Cost Price (CP)** of the second batch (20 kg at ₹ 14.25/kg) = $20 \times 14.25 = 285$ * **Total Cost Price** of the 50 kg mixture = $345 + 285 = 630$ * To achieve a 30% profit, the Total Selling Price (SP) needed = $630 \times 1.30 = 819$ * **SP per kg** = $\frac{819}{50} = 16.38$ * The exact required selling price is ₹ 16.38. The closest approximate value provided in the options is ₹ 16.30. ### Exam Strategy & Shortcut Instead of calculating totals, you can find the average CP per kg directly using weighted averages: Average CP = $\frac{3 \times 11.50 + 2 \times 14.25}{5} = \frac{34.50 + 28.50}{5} = \frac{63}{5} = 12.60$. Required SP = $12.60 \times 1.30 = 16.38$. ### Common Pitfall A common mistake is finding the simple average of the rates ($\frac{11.50 + 14.25}{2}$) instead of using the weighted average based on the quantities purchased. ### Final Answer Therefore, the correct answer is **₹ 16.30**.