Two varieties of soda water with different prices is mixed in the ratio of 2:3.The price of first soda water is rs 10 per litre while the price of second soda water is ts 15 per litre, respectively. The average price of the mixture (per litre) is:

Options

A. 12
B. 13
C. 14
D. 15

Explanation

To find the average price of the mixture of two varieties of soda water, we can follow these steps:

### Step 1: Identify the Prices and Ratios
We have:
- Price of first soda water (A) = Rs. 10 per litre
- Price of second soda water (B) = Rs. 15 per litre
- Ratio of mixing = 2:3

### Step 2: Assign Variables for Quantities
Let the quantity of first soda water (A) be 2x litres and the quantity of second soda water (B) be 3x litres. Here, x is a common multiplier.

### Step 3: Calculate the Total Cost of Each Variety
- Total cost of first soda water (A) = Price of A × Quantity of A
\[ \text{Total cost of A} = 10 \times 2x = 20x \text{ Rs.} \]

- Total cost of second soda water (B) = Price of B × Quantity of B
\[ \text{Total cost of B} = 15 \times 3x = 45x \text{ Rs.} \]

### Step 4: Calculate the Total Cost of the Mixture
Now, we can find the total cost of the mixture:
\[ \text{Total cost of mixture} = \text{Total cost of A} + \text{Total cost of B} = 20x + 45x = 65x \text{ Rs.} \]

### Step 5: Calculate the Total Quantity of the Mixture
The total quantity of the mixture is:
\[ \text{Total quantity} = 2x + 3x = 5x \text{ litres.} \]

### Step 6: Calculate the Average Price of the Mixture
The average price per litre of the mixture can be calculated using the formula:
\[ \text{Average price} = \frac{\text{Total cost of mixture}}{\text{Total quantity}} = \frac{65x}{5x} = 13 \text{ Rs.} \]

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

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