`1/6` of the content of a jar containing a mixture of milk and water is taken out. The jar had initially 180 lit of milk. The quantity of milk in the resultant mixture is 100 lit more than water. What was the initial quantity of water in the jar? (in lit)

Options

A. 50
B. 40
C. 60
D. None of those given as options

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript:

### Step 1: Define the Variables
Let the initial quantity of water in the jar be \( x \) liters. We know that the initial quantity of milk is 180 liters.

### Step 2: Calculate the Total Initial Volume
The total initial volume of the mixture (milk + water) is:
\[ \text{Total Volume} = 180 + x \text{ liters} \]

### Step 3: Determine the Volume After Taking Out \( \frac{1}{6} \)
When \( \frac{1}{6} \) of the total content is taken out, the remaining volume is:
\[ \text{Remaining Volume} = \frac{5}{6} \times (180 + x) \]

### Step 4: Calculate the Remaining Milk
The quantity of milk remaining after taking out \( \frac{1}{6} \) is:
\[ \text{Remaining Milk} = \frac{5}{6} \times 180 = 150 \text{ liters} \]

### Step 5: Calculate the Remaining Water
The quantity of water remaining after taking out \( \frac{1}{6} \) is:
\[ \text{Remaining Water} = \frac{5}{6} \times x = \frac{5x}{6} \text{ liters} \]

### Step 6: Set Up the Equation
According to the problem, the quantity of milk in the resultant mixture is 100 liters more than the quantity of water. Therefore, we can set up the equation:
\[ 150 = \frac{5x}{6} + 100 \]

### Step 7: Solve the Equation
Now, let's solve for \( x \):
1. Subtract 100 from both sides:
\[ 150 - 100 = \frac{5x}{6} \]
\[ 50 = \frac{5x}{6} \]

2. Multiply both sides by 6 to eliminate the fraction:
\[ 300 = 5x \]

3. Divide both sides by 5:
\[ x = 60 \]

### Step 8: Conclusion
The initial quantity of water in the jar is \( 60 \) liters.

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