A vessel contains mixture of milk and water in the ratio of 7:1 respectively. 24 liters mixture is removed from the vessel and if the quantity of remaining milk in the vessel is 56 liters, then find quantity of water in the vessel initially.

Options

A. 11 liters
B. 15 liters
C. 12 liters
D. 9 liters

Answer

To solve the problem step by step, we will follow the logical reasoning presented in the video transcript.

### Step 1: Understand the Initial Ratio
The mixture of milk and water is in the ratio of 7:1. This means for every 8 parts of the mixture, 7 parts are milk and 1 part is water.

### Step 2: Define Variables
Let the quantity of water in the mixture be \( x \) liters. Therefore, the quantity of milk will be \( 7x \) liters.

### Step 3: Calculate Total Initial Quantity
The total quantity of the mixture can be expressed as:
\[ \text{Total mixture} = \text{Milk} + \text{Water} = 7x + x = 8x \text{ liters} \]

### Step 4: Mixture Removed
According to the problem, 24 liters of the mixture is removed. After removing this mixture, the remaining quantity of milk is 56 liters.

### Step 5: Calculate Remaining Milk
When 24 liters of the mixture is removed, the proportion of milk and water removed can be calculated based on the ratio:
- The fraction of milk in the mixture is \( \frac{7}{8} \).
- The fraction of water in the mixture is \( \frac{1}{8} \).

Thus, the quantity of milk removed when 24 liters is taken out is:
\[ \text{Milk removed} = 24 \times \frac{7}{8} = 21 \text{ liters} \]

### Step 6: Set Up the Equation
The remaining quantity of milk after removing 21 liters is given as 56 liters. Therefore, we can set up the equation:
\[ 7x - 21 = 56 \]

### Step 7: Solve for \( x \)
Now, we solve for \( x \):
\[ 7x = 56 + 21 \]
\[ 7x = 77 \]
\[ x = \frac{77}{7} = 11 \text{ liters} \]

### Step 8: Find the Initial Quantity of Water
Since \( x \) represents the quantity of water in the mixture initially, we have:
\[ \text{Quantity of water} = x = 11 \text{ liters} \]

### Final Answer
The initial quantity of water in the vessel is **11 liters**.

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