A jar of mixed fruit made of pomegranate and carrot jucice contains `14.4` litre juice. If the ratio of pomegranate juice to carrot juice is `3:5,` find the quantity of pomegranate juice in the jar in milliliters.

Answer

To solve the problem step by step, we need to find the quantity of pomegranate juice in the jar given the total volume and the ratio of pomegranate juice to carrot juice.

### Step 1: Understand the given information
We know that:
- The total volume of juice in the jar is 14.4 liters.
- The ratio of pomegranate juice to carrot juice is 3:5.

### Step 2: Set up the variables based on the ratio
Let:
- The quantity of pomegranate juice be \(3x\) liters.
- The quantity of carrot juice be \(5x\) liters.

### Step 3: Write the equation for the total volume
According to the problem, the total volume of juice is the sum of pomegranate juice and carrot juice:
\[ 3x + 5x = 14.4 \]
This simplifies to:
\[ 8x = 14.4 \]

### Step 4: Solve for \(x\)
To find \(x\), divide both sides of the equation by 8:
\[ x = \frac{14.4}{8} \]

Calculating this gives:
\[ x = 1.8 \]

### Step 5: Calculate the quantity of pomegranate juice
Now that we have \(x\), we can find the quantity of pomegranate juice:
\[ \text{Pomegranate juice} = 3x = 3 \times 1.8 = 5.4 \text{ liters} \]

### Step 6: Convert liters to milliliters
Since we need the answer in milliliters, we convert liters to milliliters by multiplying by 1000:
\[ 5.4 \text{ liters} = 5.4 \times 1000 = 5400 \text{ milliliters} \]

### Final Answer
The quantity of pomegranate juice in the jar is **5400 milliliters**.

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