Nikita bought 30 kg of wheat at the rate of ₹ 9.50 per kg and 40 kg of wheat at the rate of ₹ 8.50 per kg and mixed them. She sold the mixture at the rate of ₹ 8.90 per kg. Her total profit or loss in the transaction was

### Concept & Weighted Average and Profit To determine total profit or loss, we must find the Total Cost Price (CP) of all the components mixed and compare it against the Total Selling Price (SP) of the complete mixture. $$\text{Total Profit/Loss} = \text{Total SP} - \text{Total CP}$$ ### Step-by-Step Solution * **Calculate Total Cost Price (CP):** * Cost of first variety = $30 \text{ kg} \times ₹ 9.50/\text{kg} = ₹ 285$ * Cost of second variety = $40 \text{ kg} \times ₹ 8.50/\text{kg} = ₹ 340$ * Total CP = $285 + 340 = ₹ 625$ * **Calculate Total Selling Price (SP):** * Total weight of mixture = $30 \text{ kg} + 40 \text{ kg} = 70 \text{ kg}$ * Total SP = $70 \text{ kg} \times ₹ 8.90/\text{kg} = ₹ 623$ * **Determine Profit or Loss:** * Since CP (₹ 625) > SP (₹ 623), there is a loss. * Loss = $CP - SP = 625 - 623 = ₹ 2$ ### Exam Strategy & Shortcut Work with margins directly on the mixture average. Average cost price per kg = $(30 \times 9.5 + 40 \times 8.5) / 70 = (285 + 340) / 70 = 625 / 70 \approx ₹ 8.928$. She sells at ₹ 8.90, so there is a loss. Exact total loss = $70 \times (625/70 - 8.90) = 625 - 623 = 2$. ### Common Pitfall A common mistake is finding the simple average of the prices ($(9.50 + 8.50) / 2 = 9.00$) instead of the weighted average based on quantities. ### Final Answer Therefore, the correct answer is **₹ 2 loss**.