A mixture contains milk and water In the ratio of `7 : 2`. On adding 6 litres of water, the ratio of milk and water becomes `7:5`. Then quantity of water in the final mixture will be-

Options

A. 10 litre
B. 4 litre
C. 12 litre
D. None of these

Answer

To solve the problem step-by-step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the initial ratio
The initial ratio of milk to water is given as \(7:2\). We can express the quantities of milk and water in terms of a variable \(x\):
- Milk = \(7x\) liters
- Water = \(2x\) liters

### Step 2: Add water and set up the new ratio
When 6 liters of water is added, the new quantity of water becomes:
- New Water = \(2x + 6\) liters

The new ratio of milk to water is given as \(7:5\). We can set up the equation based on this new ratio:
\[ \frac{7x}{2x + 6} = \frac{7}{5} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 7x \cdot 5 = 7 \cdot (2x + 6) \]
This simplifies to:
\[ 35x = 14x + 42 \]

### Step 4: Solve for \(x\)
Now, we will isolate \(x\):
\[ 35x - 14x = 42 \]
\[ 21x = 42 \]
\[ x = 2 \]

### Step 5: Calculate the quantity of water in the final mixture
Now that we have \(x\), we can find the initial quantity of water:
- Initial Water = \(2x = 2 \cdot 2 = 4\) liters

After adding 6 liters of water, the total quantity of water in the final mixture is:
\[ \text{Final Water} = 2x + 6 = 4 + 6 = 10 \text{ liters} \]

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

---