c) A fruit seller sold 50 kg of oranges at the rate of Rs 80 per \( \mathbf{k g} \) and gained Rs 800 . (i) Find the selling price of 50 kg of oranges. (ii) At what rate of price did he buy the oranges?

Let's solve the problem step by step. ### Given: - **Quantity sold:** 50 kg of oranges - **Selling price per kg (SP/kg):** Rs 80 - **Total profit (Gain):** Rs 800 ### (i) Find the Selling Price of 50 kg of Oranges. The **selling price (SP)** for the total quantity can be calculated as: \[ \text{SP} = \text{Quantity} \times \text{Selling Price per kg} = 50 \, \text{kg} \times \text{Rs } 80/\text{kg} = \text{Rs } 4000 \] **Answer:** The selling price of 50 kg of oranges is **Rs 4000**. --- ### (ii) At What Rate Did He Buy the Oranges? To find the **cost price (CP)** per kg, we'll use the relationship between selling price, cost price, and profit. \[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \] Given that the total profit is Rs 800, we can express it as: \[ 800 = \text{Total SP} - \text{Total CP} \] We already know the **Total SP** is Rs 4000. Let the **Total CP** be \( \text{CP}_{\text{total}} \). \[ 800 = 4000 - \text{CP}_{\text{total}} \\ \text{CP}_{\text{total}} = 4000 - 800 = 3200 \, \text{Rs} \] Now, find the **Cost Price per kg (CP/kg)**: \[ \text{CP/kg} = \frac{\text{Total CP}}{\text{Quantity}} = \frac{3200}{50} = \text{Rs } 64/\text{kg} \] **Answer:** The buying price was **Rs 64 per kg**. ### Summary: 1. **Selling Price of 50 kg:** Rs 4000 2. **Buying Price per kg:** Rs 64