A trader mixes three varieties of groundnuts costing Rs. 50., Rs. 20 and Rs. 30 per kg in the ratio 2 : 4 : 3 in terms of weight, and sells the mixture of Rs. 33 per kg. What percentage of profit does he make?

Options

A. `8%`
B. `9%`
C. `10%`
D. None of these

Answer

To solve the problem step-by-step, we will calculate the cost price (CP) of the mixture, the selling price (SP), and then determine the percentage of profit.

### Step 1: Determine the total cost of each variety of groundnut in the mixture.

The trader mixes three varieties of groundnuts in the ratio of 2:4:3.

- Cost of first variety (Rs. 50 per kg) = 2 parts
- Cost of second variety (Rs. 20 per kg) = 4 parts
- Cost of third variety (Rs. 30 per kg) = 3 parts

### Step 2: Calculate the total cost for each variety.

1. For the first variety:
\[ \text{Cost} = 2 \times 50 = 100 \text{ Rs.} \]

2. For the second variety:
\[ \text{Cost} = 4 \times 20 = 80 \text{ Rs.} \]

3. For the third variety:
\[ \text{Cost} = 3 \times 30 = 90 \text{ Rs.} \]

### Step 3: Calculate the total cost of the mixture.

Now, add the costs of all three varieties:
\[ \text{Total Cost} = 100 + 80 + 90 = 270 \text{ Rs.} \]

### Step 4: Calculate the total parts in the mixture.

The total parts in the mixture are:
\[ 2 + 4 + 3 = 9 \text{ parts.} \]

### Step 5: Calculate the cost price (CP) of 1 kg of the mixture.

To find the CP of 1 kg of the mixture:
\[ \text{CP of 1 kg} = \frac{\text{Total Cost}}{\text{Total Parts}} = \frac{270}{9} = 30 \text{ Rs.} \]

### Step 6: Determine the selling price (SP) of the mixture.

The selling price of the mixture is given as:
\[ \text{SP} = 33 \text{ Rs.} \]

### Step 7: Calculate the profit.

Profit can be calculated using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} = 33 - 30 = 3 \text{ Rs.} \]

### Step 8: Calculate the percentage of profit.

The percentage of profit is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{3}{30}\right) \times 100 = 10\% \]

### Final Answer:
The percentage of profit made by the trader is **10%**.

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