A company blends two varieties of tea from two different tea gardens, one variety costing Rs. 20 per kg and other Rs. 25 per kg, in the ratio 5 : 4. He sells the blended tea at Rs. 23 per kg. Find his profit per cent :

Options

A. 5% profit
B. 3.5% loss
C. 3.5% profit
D. No profit, no loss

Answer

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

### Step 1: Determine the cost of each variety of tea
Let the first variety of tea cost Rs. 20 per kg and the second variety cost Rs. 25 per kg.

### Step 2: Calculate the total cost of the blended tea
The tea is blended in the ratio of 5:4. This means for every 5 kg of the first variety, there are 4 kg of the second variety.

- Cost of 5 kg of the first variety:
\[ 5 \text{ kg} \times 20 \text{ Rs/kg} = 100 \text{ Rs} \]

- Cost of 4 kg of the second variety:
\[ 4 \text{ kg} \times 25 \text{ Rs/kg} = 100 \text{ Rs} \]

- Total cost of the blended tea:
\[ 100 \text{ Rs} + 100 \text{ Rs} = 200 \text{ Rs} \]

### Step 3: Calculate the total weight of the blended tea
The total weight of the blended tea is:
\[ 5 \text{ kg} + 4 \text{ kg} = 9 \text{ kg} \]

### Step 4: Calculate the selling price of the blended tea
The selling price of the blended tea is Rs. 23 per kg. Therefore, the total selling price for 9 kg is:
\[ 9 \text{ kg} \times 23 \text{ Rs/kg} = 207 \text{ Rs} \]

### Step 5: Calculate the profit
Profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 207 \text{ Rs} - 200 \text{ Rs} = 7 \text{ Rs} \]

### Step 6: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{7 \text{ Rs}}{200 \text{ Rs}} \right) \times 100 = 3.5\% \]

### Final Answer
The profit percentage is **3.5%**.

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