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 the above

Answer

To solve the problem, we need to find the quantity of water in the final mixture after adding 6 liters of water to the original mixture of milk and water.

### Step-by-step Solution:

1. **Define the initial quantities**:
Let the initial quantities of milk and water be represented as:
- Milk = 7k
- Water = 2k
Here, k is a common multiplier.

2. **Set up the equation after adding water**:
When we add 6 liters of water to the mixture, the new quantity of water becomes:
- New Water = 2k + 6

3. **Establish the new ratio**:
According to the problem, after adding 6 liters of water, the ratio of milk to water becomes 7:5. Therefore, we can set up the equation:
\[ \frac{7k}{2k + 6} = \frac{7}{5} \]

4. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives us:
\[ 7 \times (2k + 6) = 5 \times 7k \]
Simplifying this, we have:
\[ 14k + 42 = 35k \]

5. **Rearranging the equation**:
Rearranging gives:
\[ 35k - 14k = 42 \]
Simplifying further, we find:
\[ 21k = 42 \]

6. **Solve for k**:
Dividing both sides by 21, we get:
\[ k = 2 \]

7. **Calculate the initial quantities**:
Now that we have k, we can find the initial quantities of milk and water:
- Milk = 7k = 7 * 2 = 14 liters
- Water = 2k = 2 * 2 = 4 liters

8. **Find the final quantity of water**:
After adding 6 liters of water, the total quantity of water in the final mixture is:
\[ \text{Final Water} = \text{Initial Water} + 6 = 4 + 6 = 10 \text{ liters} \]

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