A vessel of 160 litre is filled with Milk and Water, 70% of Milk and 30% of Water is taken out of the vessel. After this task, it is found that vessel is now filled by 55% quantity of Milk and Water. What is the original quantity of milk and water in the vessel respectively?

Options

A. 60, 100
B. 100,60
C. 70,90
D. 90,70

Answer

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

### Step 1: Understand the problem
We have a vessel with a total capacity of 160 liters filled with a mixture of milk and water. We need to find the original quantities of milk and water in the vessel.

### Step 2: Define variables
Let:
- \( x \) = original quantity of milk (in liters)
- \( 160 - x \) = original quantity of water (in liters)

### Step 3: Calculate the quantities taken out
According to the problem:
- 70% of the milk is taken out:
\[ \text{Milk taken out} = 0.7x \]
- 30% of the water is taken out:
\[ \text{Water taken out} = 0.3(160 - x) = 48 - 0.3x \]

### Step 4: Calculate the remaining quantities
After taking out the specified quantities, the remaining quantities in the vessel are:
- Remaining milk:
\[ \text{Remaining milk} = x - 0.7x = 0.3x \]
- Remaining water:
\[ \text{Remaining water} = (160 - x) - (48 - 0.3x) = 160 - x - 48 + 0.3x = 112 - 0.7x \]

### Step 5: Set up the equation based on the remaining mixture
After the removal, it is stated that the vessel is now filled with 55% of the total capacity (160 liters):
\[ \text{Total remaining mixture} = 0.55 \times 160 = 88 \text{ liters} \]

Thus, we can write the equation:
\[ 0.3x + (112 - 0.7x) = 88 \]

### Step 6: Simplify the equation
Combine like terms:
\[ 0.3x + 112 - 0.7x = 88 \]
\[ -0.4x + 112 = 88 \]

### Step 7: Solve for \( x \)
Subtract 112 from both sides:
\[ -0.4x = 88 - 112 \]
\[ -0.4x = -24 \]
Now, divide by -0.4:
\[ x = \frac{-24}{-0.4} = 60 \]

### Step 8: Find the quantity of water
Now, substitute \( x \) back to find the quantity of water:
\[ \text{Water} = 160 - x = 160 - 60 = 100 \]

### Conclusion
The original quantities are:
- Quantity of Milk = \( 60 \) liters
- Quantity of Water = \( 100 \) liters

### Final Answer
- Milk: 60 liters
- Water: 100 liters

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