A retailer bought 30 kg of rice at a discount of `20%` on the marked price. Besides, he was given 8 kg of rice free of cost, by the wholesaler for purchasing a bulk quantity. If the retailer sold the entire quantity of rice at the marked price to his customers, what was his profit per cent ?

Options

A. `45 1/3%`
B. `52 2/3%`
C. `58 1/3%`
D. `42 2/3%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price of 30 kg of Rice
- Let the marked price (MP) of the rice be 100 rupees.
- The retailer receives a discount of 20% on the marked price.
- Therefore, the cost price (CP) after the discount is:
\[ CP = MP - (20\% \text{ of } MP) = 100 - 20 = 80 \text{ rupees} \]

### Step 2: Calculate the Total Cost Price for 30 kg of Rice
- The retailer bought 30 kg of rice at a cost price of 80 rupees per kg.
- Thus, the total cost price for 30 kg is:
\[ \text{Total CP} = 30 \text{ kg} \times 80 \text{ rupees/kg} = 2400 \text{ rupees} \]

### Step 3: Calculate the Total Quantity of Rice
- The retailer also received 8 kg of rice free of cost.
- Therefore, the total quantity of rice the retailer has is:
\[ \text{Total Quantity} = 30 \text{ kg} + 8 \text{ kg} = 38 \text{ kg} \]

### Step 4: Determine the Selling Price of the Rice
- The retailer sells all the rice at the marked price of 100 rupees per kg.
- Thus, the total selling price (SP) for 38 kg is:
\[ \text{Total SP} = 38 \text{ kg} \times 100 \text{ rupees/kg} = 3800 \text{ rupees} \]

### Step 5: Calculate the Profit
- The profit can be calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} = 3800 \text{ rupees} - 2400 \text{ rupees} = 1400 \text{ rupees} \]

### Step 6: Calculate the Profit Percentage
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \]
- Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{1400}{2400} \right) \times 100 = \frac{1400 \times 100}{2400} = \frac{140000}{2400} = 58.33\% \]

### Conclusion
The profit percentage is \( 58 \frac{1}{3} \% \).