10 kg of rice priced at Rs. 12 per kg is mixed with 6 kg of rice priced at Rs. 16 per kg. Find the average price of the whole mixture?

Options

A. Rs. 14 per kg
B. Rs. 14.50 per kg
C. Rs. 13 per kg
D. Rs. 13.50 per kg

Answer

To find the average price of the mixture of two types of rice, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the quantities and prices of the two types of rice:**
- First type: 10 kg of rice priced at Rs. 12 per kg.
- Second type: 6 kg of rice priced at Rs. 16 per kg.

2. **Calculate the total cost of each type of rice:**
- Total cost of the first type:
\[ \text{Cost of first type} = \text{Quantity} \times \text{Price per kg} = 10 \, \text{kg} \times 12 \, \text{Rs/kg} = 120 \, \text{Rs} \]
- Total cost of the second type:
\[ \text{Cost of second type} = \text{Quantity} \times \text{Price per kg} = 6 \, \text{kg} \times 16 \, \text{Rs/kg} = 96 \, \text{Rs} \]

3. **Calculate the total cost of the mixture:**
\[ \text{Total cost} = \text{Cost of first type} + \text{Cost of second type} = 120 \, \text{Rs} + 96 \, \text{Rs} = 216 \, \text{Rs} \]

4. **Calculate the total quantity of the mixture:**
\[ \text{Total quantity} = 10 \, \text{kg} + 6 \, \text{kg} = 16 \, \text{kg} \]

5. **Calculate the average price of the mixture:**
\[ \text{Average price} = \frac{\text{Total cost}}{\text{Total quantity}} = \frac{216 \, \text{Rs}}{16 \, \text{kg}} = 13.5 \, \text{Rs/kg} \]

### Final Answer:
The average price of the whole mixture is Rs. 13.5 per kg.

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