Two blends of a commodity cost ing Rs. 35 and Rs. 40 per kg. respectively are mixed in the ra tio 2: 3 by weight. If one-fifth of the mixture is sold at Rs. 46 per kg and the remaining at the rate of Rs. 55 per kg. the profit percent is

Options

A. 50
B. 30
C. 40
D. 20

Answer

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

### Step 1: Determine the cost of each blend
- The first blend costs Rs. 35 per kg.
- The second blend costs Rs. 40 per kg.

### Step 2: Calculate the total cost of the blends in the given ratio
- The ratio of the blends is 2:3.
- Let's assume we take 2 kg of the first blend and 3 kg of the second blend.
- Cost of the first blend:
\[ 2 \, \text{kg} \times 35 \, \text{Rs/kg} = 70 \, \text{Rs} \]
- Cost of the second blend:
\[ 3 \, \text{kg} \times 40 \, \text{Rs/kg} = 120 \, \text{Rs} \]

### Step 3: Calculate the total cost price of the mixture
- Total cost price of the mixture:
\[ 70 \, \text{Rs} + 120 \, \text{Rs} = 190 \, \text{Rs} \]
- Total weight of the mixture:
\[ 2 \, \text{kg} + 3 \, \text{kg} = 5 \, \text{kg} \]

### Step 4: Calculate the selling price of the mixture
- One-fifth of the mixture is sold, which is:
\[ \frac{1}{5} \times 5 \, \text{kg} = 1 \, \text{kg} \]
- Selling price of 1 kg at Rs. 46:
\[ 1 \, \text{kg} \times 46 \, \text{Rs/kg} = 46 \, \text{Rs} \]
- The remaining mixture is:
\[ 5 \, \text{kg} - 1 \, \text{kg} = 4 \, \text{kg} \]
- Selling price of 4 kg at Rs. 55:
\[ 4 \, \text{kg} \times 55 \, \text{Rs/kg} = 220 \, \text{Rs} \]

### Step 5: Calculate the total selling price
- Total selling price:
\[ 46 \, \text{Rs} + 220 \, \text{Rs} = 266 \, \text{Rs} \]

### Step 6: Calculate the profit
- Profit is given by:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 266 \, \text{Rs} - 190 \, \text{Rs} = 76 \, \text{Rs} \]

### Step 7: Calculate the profit percentage
- Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{76}{190} \right) \times 100 \]
- Simplifying this:
\[ \text{Profit Percentage} = \frac{76 \times 100}{190} = \frac{7600}{190} \approx 40\% \]

### Final Answer
The profit percentage is approximately **40%**.

---