Two varieties of milk with different prices is mixed in the ratio 2 : 3. The price of 1st type of milk is Rs 10 per litre while the price of 2nd type of milk is Rs. 15 per litre. The average price of the mixture

Options

A. Rs. 11 per litre
B. Rs. 12 per litre
C. Rs. 13 per litre
D. Rs. 14 per litre

Answer

To find the average price of the mixture of two varieties of milk mixed in the ratio of 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Prices and Ratios:**
- Price of the first type of milk (P1) = Rs 10 per litre
- Price of the second type of milk (P2) = Rs 15 per litre
- Ratio of mixing = 2:3

2. **Assign Variables for the Average Price:**
- Let the average price of the mixture be X.

3. **Set Up the Equation Using the Mixing Formula:**
- According to the mixing formula, we can set up the following equations based on the ratio:
\[ \frac{X - P1}{P2 - X} = \frac{3}{2} \]
- Substituting the values:
\[ \frac{X - 10}{15 - X} = \frac{3}{2} \]

4. **Cross-Multiply to Solve for X:**
- Cross-multiplying gives us:
\[ 2(X - 10) = 3(15 - X) \]
- Expanding both sides:
\[ 2X - 20 = 45 - 3X \]

5. **Combine Like Terms:**
- Rearranging the equation:
\[ 2X + 3X = 45 + 20 \]
\[ 5X = 65 \]

6. **Solve for X:**
- Dividing both sides by 5:
\[ X = \frac{65}{5} = 13 \]

7. **Conclusion:**
- The average price of the mixture is Rs 13 per litre.

### Final Answer:
The average price of the mixture is Rs 13 per litre.