A mixture contains milk and water in the atio of 5:6. on adding 8 litres of water, the ratio of milk and water becomes 1:2. find the quantity of the milk in the mixture. (in litres)

Options

A. 12
B. 10
C. 14
D. 8

Explanation

To solve the problem step by step, we will denote the quantities of milk and water in the mixture using a variable \( k \).

### Step 1: Define the quantities of milk and water
Given the ratio of milk to water is 5:6, we can express the quantities as:
- Milk = \( 5k \)
- Water = \( 6k \)

### Step 2: Add the additional water
According to the problem, we add 8 liters of water to the mixture. Therefore, the new quantity of water becomes:
- New Water = \( 6k + 8 \)

### Step 3: Set up the new ratio
After adding the water, the new ratio of milk to water is given as 1:2. We can express this as:
\[ \frac{\text{Milk}}{\text{New Water}} = \frac{1}{2} \]
Substituting the quantities we have:
\[ \frac{5k}{6k + 8} = \frac{1}{2} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 5k \cdot 2 = 1 \cdot (6k + 8) \]
This simplifies to:
\[ 10k = 6k + 8 \]

### Step 5: Solve for \( k \)
Now, we will isolate \( k \):
\[ 10k - 6k = 8 \]
\[ 4k = 8 \]
\[ k = \frac{8}{4} = 2 \]

### Step 6: Calculate the quantity of milk
Now that we have \( k \), we can find the quantity of milk:
\[ \text{Milk} = 5k = 5 \times 2 = 10 \text{ liters} \]

### Final Answer
The quantity of milk in the mixture is **10 liters**.

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