In a mixture of 45 L, the ratio of milk and water is 2 : 1. If this ratio is to be 3 : 2, the quantity of water to be further added is

Options

A. 3L
B. 5L
C. 8L
D. None of these

Answer

To solve the problem step by step, we need to find out how much water needs to be added to change the ratio of milk to water in a 45 L mixture from 2:1 to 3:2.

### Step 1: Determine the current quantities of milk and water.
The total volume of the mixture is 45 L, and the ratio of milk to water is 2:1.

To find the quantities of milk and water:
- Total parts in the ratio = 2 (milk) + 1 (water) = 3 parts
- Quantity of milk = (2/3) * 45 L = 30 L
- Quantity of water = (1/3) * 45 L = 15 L

### Step 2: Set up the new ratio.
We want to change the ratio of milk to water to 3:2.

Let the quantity of water to be added be \( x \) L. After adding \( x \) L of water, the new quantity of water will be \( 15 + x \) L, while the quantity of milk remains the same at 30 L.

### Step 3: Write the equation based on the new ratio.
According to the new ratio of 3:2:
\[ \frac{30}{15 + x} = \frac{3}{2} \]

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:
\[ 30 \cdot 2 = 3 \cdot (15 + x) \]
\[ 60 = 45 + 3x \]

### Step 5: Isolate \( x \).
Subtract 45 from both sides:
\[ 60 - 45 = 3x \]
\[ 15 = 3x \]
Now, divide by 3:
\[ x = 5 \]

### Conclusion:
The quantity of water to be further added is **5 L**.

---