A mixture contains milk and honey in the ratio `7:1`. On adding 6 litre of honey, the ratio of milk to honey becomes `7:2` the quantity of milk in the mixture is ?

Options

A. 40l
B. 50l
C. 44l
D. None of these

Explanation

To solve the problem, we need to determine the quantity of milk in the mixture given the initial ratio of milk to honey and the changes made to the mixture. Let's break it down step by step.

### Step 1: Understand the initial ratio
The initial ratio of milk to honey is given as 7:1. This means for every 7 parts of milk, there is 1 part of honey.

### Step 2: Define variables
Let the quantity of honey in the mixture be represented as \( x \). Therefore, the quantity of milk will be \( 7x \) (since the ratio is 7:1).

### Step 3: Adjust for the addition of honey
When 6 liters of honey is added to the mixture, the new quantity of honey becomes \( x + 6 \).

### Step 4: Set up the new ratio
After adding the honey, the new ratio of milk to honey is given as 7:2. This can be expressed mathematically as:
\[ \frac{7x}{x + 6} = \frac{7}{2} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 7x \cdot 2 = 7 \cdot (x + 6) \]
This simplifies to:
\[ 14x = 7x + 42 \]

### Step 6: Solve for \( x \)
Now, we can isolate \( x \):
\[ 14x - 7x = 42 \]
\[ 7x = 42 \]
\[ x = 6 \]

### Step 7: Calculate the quantity of milk
Now that we have \( x \), we can find the quantity of milk:
\[ \text{Quantity of milk} = 7x = 7 \cdot 6 = 42 \text{ liters} \]

### Final Answer
The quantity of milk in the mixture is **42 liters**.

---