A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk the second contains 50% water. How much milk should be mixed from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3:5 ?

Options

A. 4 litres, 4 litres
B. 6 litres, 6 litres
C. 5 litres, 7 litres
D. 7 litres, 5 litres

Answer

To solve the problem step by step, we need to determine how much milk to mix from each can to achieve a total of 12 liters of milk with a water to milk ratio of 3:5.

### Step 1: Understand the composition of each can
- **Can 1**: Contains 25% water and 75% milk.
- **Can 2**: Contains 50% water and 50% milk.

### Step 2: Set up the desired ratio
We want the final mixture to have a water to milk ratio of 3:5. This means:
- Total parts = 3 (water) + 5 (milk) = 8 parts.
- Water part = \( \frac{3}{8} \) of the total mixture.
- Milk part = \( \frac{5}{8} \) of the total mixture.

### Step 3: Calculate the total volume of water and milk in the final mixture
Since we want a total of 12 liters:
- Water = \( \frac{3}{8} \times 12 = 4.5 \) liters
- Milk = \( \frac{5}{8} \times 12 = 7.5 \) liters

### Step 4: Let x be the amount of milk taken from Can 1 and y be the amount from Can 2
We need to find values for \( x \) and \( y \) such that:
1. \( x + y = 12 \) (total volume)
2. The amount of water from both cans equals 4.5 liters.

### Step 5: Calculate the amount of water in each can
- Water from Can 1 (25% of x): \( 0.25x \)
- Water from Can 2 (50% of y): \( 0.50y \)

### Step 6: Set up the equation for the amount of water
From the water equation:
\[ 0.25x + 0.50y = 4.5 \]

### Step 7: Substitute y from the first equation into the water equation
From \( x + y = 12 \), we can express \( y \) as:
\[ y = 12 - x \]

Substituting \( y \) into the water equation:
\[ 0.25x + 0.50(12 - x) = 4.5 \]

### Step 8: Simplify and solve for x
Expanding the equation:
\[ 0.25x + 6 - 0.50x = 4.5 \]
Combine like terms:
\[ -0.25x + 6 = 4.5 \]
Subtract 6 from both sides:
\[ -0.25x = -1.5 \]
Divide by -0.25:
\[ x = 6 \]

### Step 9: Find y
Using \( y = 12 - x \):
\[ y = 12 - 6 = 6 \]

### Step 10: Conclusion
The vendor should mix 6 liters from Can 1 and 6 liters from Can 2.

### Summary of the solution:
- From Can 1: 6 liters
- From Can 2: 6 liters