A retailer bought 20 kg tea at a discount of `10%`. Besides 1 kg tea was freely offered to him by the wholesaler at the purchase of 20 kg tea. Now, he sells all the tea at the marked price to a customer. What is profit percentage of retailer?

Options

A. `30%`
B. `12%`
C. `16.66%`
D. none of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price of the Tea
The retailer bought 20 kg of tea at a 10% discount. Let's assume the marked price (MP) of tea is ₹10 per kg.

- **Marked Price (MP) = ₹10/kg**
- **Discount = 10% of MP = 10% of ₹10 = ₹1**
- **Cost Price (CP) after discount = MP - Discount = ₹10 - ₹1 = ₹9/kg**

Now, calculate the total cost for 20 kg of tea:

\[ \text{Total Cost Price (CP)} = \text{Cost Price per kg} \times \text{Quantity} = ₹9 \times 20 \text{ kg} = ₹180 \]

### Step 2: Calculate the Total Quantity of Tea
The wholesaler offers an additional 1 kg of tea for free when the retailer buys 20 kg. Therefore, the total quantity of tea the retailer has is:

\[ \text{Total Quantity} = 20 \text{ kg} + 1 \text{ kg} = 21 \text{ kg} \]

### Step 3: Determine the Selling Price of the Tea
The retailer sells all the tea at the marked price of ₹10 per kg. Therefore, the total selling price (SP) for 21 kg of tea is:

\[ \text{Total Selling Price (SP)} = \text{Selling Price per kg} \times \text{Total Quantity} = ₹10 \times 21 \text{ kg} = ₹210 \]

### Step 4: Calculate the Profit
Profit can be calculated using the formula:

\[ \text{Profit} = \text{Total Selling Price} - \text{Total Cost Price} = ₹210 - ₹180 = ₹30 \]

### Step 5: Calculate the Profit Percentage
Profit percentage can be calculated using the formula:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total Cost Price}} \right) \times 100 = \left( \frac{₹30}{₹180} \right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = \left( \frac{30}{180} \right) \times 100 = \frac{1}{6} \times 100 \approx 16.67\% \]

### Final Answer
The profit percentage of the retailer is approximately **16.67%**.

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