A trader mixes three varieties of groundnuts costing ₹ 50, ₹ 20 and ₹ 30 per kg in the ratio 2 : 4 : 3 in terms of weight, and sells the mixture at ₹ 33 per kg. What percentage of profit does he make?

### Concept & Profit Percentage of Multiple Mixtures When more than two items are mixed, the principle remains the same. Calculate the total cost price using the given ratio as absolute weights, determine the total cost, compare it to the total selling price, and extract the profit margin. $$Total\ CP = \sum (Ratio \times Rate)$$ ### Step-by-Step Solution * Let the quantities of the three varieties be 2 kg, 4 kg, and 3 kg. Total quantity = 9 kg. * **Total Cost Price (CP)** = $(2 \times 50) + (4 \times 20) + (3 \times 30)$ * Total CP = $100 + 80 + 90 = 270$ * **Cost Price (CP) per kg** = $\frac{270}{9} = 30$ * **Selling Price (SP) per kg** = 33 * **Profit** per kg = $33 - 30 = 3$ * **Profit Percentage** = $\left( \frac{Profit}{CP} \right) \times 100 = \left(\frac{3}{30}\right) \times 100 = 10\%$ ### Exam Strategy & Shortcut By treating the ratio numbers directly as weights (2 kg, 4 kg, 3 kg), you skip unnecessary algebraic variables. This immediately gives you a total cost of 270 for 9 kg, yielding a neat average of 30, which compares perfectly with the SP of 33 for a rapid calculation. ### Common Pitfall A common error is to calculate the profit margin relative to the selling price instead of the cost price, arriving at $\frac{3}{33} = 9.09\%$, which is incorrect. ### Final Answer Therefore, the correct answer is **10%**.