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?

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### 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
**Solutions:** 1. **Selling Price of 50 kg of Oranges:** Rs 4000 2. **Buying Price per kg of Oranges:** Rs 64

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?

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