A tank contains a mixture of 70 lt of milk and water. `65%` of the milk and `30 %` of the water are withdrawn. Therefore` 60% `part of the tank is remaining. Find the initial quantity of milk and water in the tank.

Answer

To solve the problem step by step, we will analyze the situation with the given percentages of milk and water that were withdrawn from the tank.

### Step 1: Understand the initial quantities
The tank contains a total of 70 liters of a mixture of milk and water. We need to find the initial quantities of milk and water.

### Step 2: Define the initial quantities
Let the initial quantity of milk be \( M \) liters and the initial quantity of water be \( W \) liters. We know that:
\[ M + W = 70 \quad \text{(1)} \]

### Step 3: Calculate the quantities withdrawn
According to the problem:
- 65% of the milk is withdrawn.
- 30% of the water is withdrawn.

The quantities withdrawn can be expressed as:
- Milk withdrawn = \( 0.65M \)
- Water withdrawn = \( 0.30W \)

### Step 4: Calculate the remaining quantities
After withdrawing the specified amounts, the remaining quantities of milk and water are:
- Remaining milk = \( M - 0.65M = 0.35M \)
- Remaining water = \( W - 0.30W = 0.70W \)

### Step 5: Calculate the total remaining mixture
The total remaining mixture in the tank is:
\[ 0.35M + 0.70W \]

According to the problem, this remaining mixture constitutes 60% of the original 70 liters:
\[ 0.35M + 0.70W = 0.60 \times 70 \]
\[ 0.35M + 0.70W = 42 \quad \text{(2)} \]

### Step 6: Set up the equations
Now we have two equations:
1. \( M + W = 70 \) (from step 2)
2. \( 0.35M + 0.70W = 42 \) (from step 5)

### Step 7: Solve the equations
From equation (1), we can express \( W \) in terms of \( M \):
\[ W = 70 - M \]

Substituting \( W \) in equation (2):
\[ 0.35M + 0.70(70 - M) = 42 \]
\[ 0.35M + 49 - 0.70M = 42 \]
\[ -0.35M + 49 = 42 \]
\[ -0.35M = 42 - 49 \]
\[ -0.35M = -7 \]
\[ M = \frac{-7}{-0.35} \]
\[ M = 20 \]

Now substituting \( M \) back into equation (1) to find \( W \):
\[ W = 70 - 20 = 50 \]

### Step 8: Conclusion
The initial quantities in the tank were:
- Milk = 20 liters
- Water = 50 liters

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