Manish purchased 25 kg of rice @ ₹ 32 per kg and 15 kg of rice @ ₹ 36 per kg. He mixed the two varieties of rice and sold it @ ₹ 40.20 per kg. What is the percent profit earned?

### Concept & Profit Percentage in Mixtures The profit percentage is found by determining the overall cost price of the combined mixture, the overall selling price, and then applying the standard profit percentage formula. $$\text{Profit \%} = \left( \frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \right) \times 100$$ ### Step-by-Step Solution * **Calculate Total Cost Price (CP):** * Cost of first variety = $25 \text{ kg} \times 32 = ₹ 800$ * Cost of second variety = $15 \text{ kg} \times 36 = ₹ 540$ * Total CP = $800 + 540 = ₹ 1340$ * **Calculate Total Selling Price (SP):** * Total quantity = $25 + 15 = 40 \text{ kg}$ * Total SP = $40 \text{ kg} \times 40.20 = ₹ 1608$ * **Calculate Profit:** * Profit = $\text{Total SP} - \text{Total CP} = 1608 - 1340 = ₹ 268$ * **Calculate Profit Percentage:** * $\text{Profit \%} = \frac{268}{1340} \times 100$ * $\text{Profit \%} = \frac{26800}{1340} = 20\%$ ### Exam Strategy & Shortcut Instead of dealing with large total values, simplify the ratio of quantities. Quantities are $25\text{kg}$ and $15\text{kg}$, which simplifies to a $5:3$ ratio. Average CP = $\frac{5 \times 32 + 3 \times 36}{8} = \frac{160 + 108}{8} = \frac{268}{8} = 33.5$. SP = $40.20$. Profit margin per kg = $40.20 - 33.50 = 6.70$. Profit % = $(\frac{6.70}{33.50}) \times 100 = (\frac{67}{335}) \times 100 = \frac{1}{5} \times 100 = 20\%$. ### Common Pitfall Miscalculating decimals when multiplying $40 \times 40.20$ is a frequent computational error. Always ensure to shift the decimal correctly. ### Final Answer Therefore, the correct answer is **20**.