The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

Options

A. a. 54
B. b. 18
C. c. 17
D. d. 78

Explanation

To find the price per kg of the mixed variety of rice when Type 1 rice costs Rs. 15 per kg and Type 2 rice costs Rs. 20 per kg, mixed in the ratio of 2:3, we can follow these steps:

### Step 1: Identify the quantities of rice types in the mixture
Let’s assume we take 2 kg of Type 1 rice and 3 kg of Type 2 rice. This is based on the given ratio of 2:3.

### Step 2: Calculate the total cost of each type of rice
- Cost of Type 1 rice (2 kg):
\[ \text{Cost of Type 1} = 2 \, \text{kg} \times 15 \, \text{Rs/kg} = 30 \, \text{Rs} \]

- Cost of Type 2 rice (3 kg):
\[ \text{Cost of Type 2} = 3 \, \text{kg} \times 20 \, \text{Rs/kg} = 60 \, \text{Rs} \]

### Step 3: Calculate the total cost of the mixture
Now, we add the costs of both types of rice:
\[ \text{Total Cost} = \text{Cost of Type 1} + \text{Cost of Type 2} = 30 \, \text{Rs} + 60 \, \text{Rs} = 90 \, \text{Rs} \]

### Step 4: Calculate the total quantity of the mixture
The total quantity of the mixture is:
\[ \text{Total Quantity} = 2 \, \text{kg} + 3 \, \text{kg} = 5 \, \text{kg} \]

### Step 5: Calculate the price per kg of the mixed rice
To find the price per kg of the mixed variety, we divide the total cost by the total quantity:
\[ \text{Price per kg} = \frac{\text{Total Cost}}{\text{Total Quantity}} = \frac{90 \, \text{Rs}}{5 \, \text{kg}} = 18 \, \text{Rs/kg} \]

### Final Answer
The price per kg of the mixed variety of rice is Rs. 18.

---