How much Pepsi at Rs. 6 a litre is added to 15 litre of 'dew' at Rs. 10 a litre so that the price of the mixture be Rs. 9 a litre?

Options

A. 5
B. 8
C. 10
D. none of these

Answer

To solve the problem step by step, we will use the method of allegations to find out how much Pepsi at Rs. 6 per liter needs to be added to 15 liters of Dew at Rs. 10 per liter so that the price of the mixture becomes Rs. 9 per liter.

### Step 1: Identify the Prices and Quantities
- Price of Pepsi = Rs. 6 per liter
- Price of Dew = Rs. 10 per liter
- Quantity of Dew = 15 liters
- Price of the mixture = Rs. 9 per liter

### Step 2: Set Up the Allegation
Using the allegation method, we can find the ratio of the quantities of Pepsi and Dew. We calculate the differences between the prices:

- Difference between Dew's price and the mixture's price:
\[ 10 - 9 = 1 \]

- Difference between the mixture's price and Pepsi's price:
\[ 9 - 6 = 3 \]

### Step 3: Write the Ratio
Now, we can write the ratio of the quantities of Dew to Pepsi:
\[ \text{Ratio of Dew to Pepsi} = 1 : 3 \]

### Step 4: Determine the Units
In the ratio 1:3, the total parts = 1 + 3 = 4 parts. Here, Dew corresponds to 3 parts and Pepsi corresponds to 1 part.

### Step 5: Calculate the Quantity of Dew
Since we know that the quantity of Dew is 15 liters, we can find out how much one part represents:
\[ \text{One part} = \frac{15 \text{ liters}}{3} = 5 \text{ liters} \]

### Step 6: Calculate the Quantity of Pepsi
Now, since Pepsi corresponds to 1 part:
\[ \text{Quantity of Pepsi} = 1 \times 5 \text{ liters} = 5 \text{ liters} \]

### Final Answer
Thus, the quantity of Pepsi that needs to be added is **5 liters**.

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