The ratio of milk and water in a pot is 1:3. If we added 9 litre milk and 9 litre water then the ratio becomes 2: 3. How much quantity of total mixture was present initially?

Options

A. 6 litre
B. 24 litre
C. 12 litre
D. 10 litre

Answer

To solve the problem step by step, we will use the information given about the ratios of milk and water.

### Step 1: Define the initial quantities
Let the initial quantity of milk be \( K \) liters. Since the ratio of milk to water is 1:3, the initial quantity of water will be \( 3K \) liters.

### Step 2: Calculate the initial total mixture
The total initial mixture is the sum of the quantities of milk and water:
\[ \text{Total initial mixture} = K + 3K = 4K \]

### Step 3: Set up the equation after adding milk and water
According to the problem, after adding 9 liters of milk and 9 liters of water, the new quantities are:
- New quantity of milk = \( K + 9 \) liters
- New quantity of water = \( 3K + 9 \) liters

The new ratio of milk to water is given as 2:3. Therefore, we can set up the equation:
\[ \frac{K + 9}{3K + 9} = \frac{2}{3} \]

### Step 4: Cross-multiply to solve for K
Cross-multiplying gives us:
\[ 3(K + 9) = 2(3K + 9) \]
Expanding both sides:
\[ 3K + 27 = 6K + 18 \]

### Step 5: Rearranging the equation
Now, we will rearrange the equation to isolate \( K \):
\[ 27 - 18 = 6K - 3K \]
\[ 9 = 3K \]
Dividing both sides by 3 gives:
\[ K = 3 \]

### Step 6: Calculate the initial total mixture
Now that we have \( K \), we can find the initial total mixture:
\[ \text{Total initial mixture} = 4K = 4 \times 3 = 12 \text{ liters} \]

### Final Answer
The initial total quantity of the mixture present in the pot was **12 liters**.

---