In first mixture, ratio of milk to water is 7: 9. After adding 24 ltr of second mixture (having ratio of water to milk 3: 5) in the first mixture, the quantity of milk and water becomes equal in the final mixture. Find the total quantity of milk in the final mixture.

Options

A. 28 ltr
B. 30 ltr
C. 36 ltr
D. 32 ltr

Answer

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Understand the Ratios
The first mixture has a ratio of milk to water as 7:9. This means for every 16 parts of the mixture (7 parts milk + 9 parts water), 7 parts are milk and 9 parts are water.

### Step 2: Define Variables
Let the quantity of the first mixture be \( x \) liters.
- Quantity of milk in the first mixture = \( \frac{7}{16}x \)
- Quantity of water in the first mixture = \( \frac{9}{16}x \)

### Step 3: Analyze the Second Mixture
The second mixture has a ratio of water to milk as 3:5. This means for every 8 parts of the mixture (3 parts water + 5 parts milk), 5 parts are milk and 3 parts are water.
- The total quantity of the second mixture is 24 liters.
- Quantity of milk in the second mixture = \( \frac{5}{8} \times 24 = 15 \) liters
- Quantity of water in the second mixture = \( \frac{3}{8} \times 24 = 9 \) liters

### Step 4: Combine the Mixtures
When the second mixture is added to the first mixture:
- Total quantity of milk in the final mixture = Milk from first mixture + Milk from second mixture
\[ \text{Total milk} = \frac{7}{16}x + 15 \]
- Total quantity of water in the final mixture = Water from first mixture + Water from second mixture
\[ \text{Total water} = \frac{9}{16}x + 9 \]

### Step 5: Set Up the Equation
According to the problem, the quantity of milk and water becomes equal in the final mixture. Therefore, we can set up the equation:
\[ \frac{7}{16}x + 15 = \frac{9}{16}x + 9 \]

### Step 6: Solve the Equation
To solve for \( x \), we rearrange the equation:
\[ 15 - 9 = \frac{9}{16}x - \frac{7}{16}x \]
\[ 6 = \frac{2}{16}x \]
\[ 6 = \frac{1}{8}x \]
\[ x = 6 \times 8 = 48 \text{ liters} \]

### Step 7: Calculate the Total Quantity of Milk in the Final Mixture
Now that we have \( x \), we can find the total quantity of milk in the final mixture:
\[ \text{Total milk} = \frac{7}{16} \times 48 + 15 \]
\[ = 21 + 15 = 36 \text{ liters} \]

### Final Answer
The total quantity of milk in the final mixture is **36 liters**.

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