A trader mixes two varieties of tea Rs 18 per Kg. and 20 per Kg. in the ratio 5: 3. he sells the entire quantity at the rate of F 21 per Kg.Find the profit percentage.

Options

A. 0.1
B. 0.12
C. 0.19
D. 0.22

Answer

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

### Step 1: Determine the quantities of each type of tea
The trader mixes two varieties of tea in the ratio of 5:3. Let's assume the total quantity of tea mixed is 8 kg (5 kg of the first variety and 3 kg of the second variety).

- Quantity of tea at Rs 18 per kg = 5 kg
- Quantity of tea at Rs 20 per kg = 3 kg

### Step 2: Calculate the total cost price (CP) of the mixture
Now, we will calculate the cost price of each variety of tea.

- Cost of 5 kg of tea at Rs 18 per kg = 5 kg × Rs 18/kg = Rs 90
- Cost of 3 kg of tea at Rs 20 per kg = 3 kg × Rs 20/kg = Rs 60

Now, add both costs to find the total cost price of the mixture:
- Total CP = Rs 90 + Rs 60 = Rs 150

### Step 3: Calculate the average cost price per kg
Now, we need to find the average cost price per kg of the mixture.

- Total quantity of tea = 5 kg + 3 kg = 8 kg
- Average CP per kg = Total CP / Total quantity = Rs 150 / 8 kg = Rs 18.75 per kg

### Step 4: Determine the selling price (SP)
The trader sells the entire quantity at Rs 21 per kg.

### Step 5: Calculate the profit
Now, we will calculate the profit made by selling the tea.

- Profit per kg = Selling Price - Average Cost Price
- Profit per kg = Rs 21 - Rs 18.75 = Rs 2.25

### Step 6: Calculate the total profit
Now, we will calculate the total profit for the entire quantity sold.

- Total profit = Profit per kg × Total quantity = Rs 2.25 × 8 kg = Rs 18

### Step 7: Calculate the profit percentage
Finally, we will calculate the profit percentage.

- Profit Percentage = (Total Profit / Total CP) × 100
- Profit Percentage = (Rs 18 / Rs 150) × 100 = 12%

Thus, the profit percentage is **12%**.

---