A vessel contains 140 litres mixture of milk and water, 60% of milk and 25% of water s taken out of the vessel it is found that the vessel is emptied by 40%. Find the difference between the initial quantities of milk and water?

Options

A. 30 litres
B. 15 litres
C. 20 litres
D. 25 litres

Answer

To solve the problem step-by-step, we will break down the information given and perform calculations accordingly.

### Step 1: Understand the Initial Mixture
The vessel contains a total of 140 liters of a mixture of milk and water. We need to determine the initial quantities of milk and water in the mixture.

### Step 2: Define Variables
Let:
- \( M \) = initial quantity of milk
- \( W \) = initial quantity of water

From the problem, we know:
- \( M + W = 140 \) liters (total mixture)

### Step 3: Determine the Percentages Taken Out
According to the problem:
- 60% of the milk is taken out
- 25% of the water is taken out

### Step 4: Calculate the Amounts Taken Out
The amounts taken out can be expressed as:
- Milk taken out = \( 0.6M \)
- Water taken out = \( 0.25W \)

### Step 5: Calculate the Total Volume Taken Out
The total volume taken out is the sum of the milk and water taken out:
\[ \text{Total taken out} = 0.6M + 0.25W \]

### Step 6: Relate the Taken Out Volume to the Vessel Volume
It is given that the vessel is emptied by 40%. Therefore, the volume taken out is:
\[ 0.4 \times 140 = 56 \text{ liters} \]

### Step 7: Set Up the Equation
Now we can set up the equation based on the total volume taken out:
\[ 0.6M + 0.25W = 56 \]

### Step 8: Solve the System of Equations
We have two equations:
1. \( M + W = 140 \)
2. \( 0.6M + 0.25W = 56 \)

From the first equation, we can express \( W \) in terms of \( M \):
\[ W = 140 - M \]

Substituting \( W \) into the second equation:
\[ 0.6M + 0.25(140 - M) = 56 \]
Expanding this gives:
\[ 0.6M + 35 - 0.25M = 56 \]
Combining like terms:
\[ 0.35M + 35 = 56 \]
Subtracting 35 from both sides:
\[ 0.35M = 21 \]
Dividing by 0.35:
\[ M = \frac{21}{0.35} = 60 \text{ liters} \]

### Step 9: Find the Quantity of Water
Now, substituting \( M \) back into the equation for \( W \):
\[ W = 140 - 60 = 80 \text{ liters} \]

### Step 10: Find the Difference Between Milk and Water
Finally, we find the difference between the initial quantities of milk and water:
\[ \text{Difference} = W - M = 80 - 60 = 20 \text{ liters} \]

### Final Answer
The difference between the initial quantities of milk and water is **20 liters**.