Two jars having a capacity of 3 and 5 litres respectively are filled with mixtures of milk and water. In the smaller jar `25%` of the mixture is milk and in the larger `25%` of the mixture is water. The jars are emptied into a 10 litre cask whose remaining capacity is filled up with water. Find the percentage of milk in the cask.

Options

A. `55%`
B. `50%`
C. `45%`
D. None of these

Answer

To solve the problem step by step, we will analyze the contents of each jar and then calculate the percentage of milk in the cask after combining the mixtures.

### Step 1: Calculate the amount of milk in the smaller jar (3 liters).
The smaller jar contains 25% milk. Therefore, the amount of milk in the smaller jar can be calculated as follows:

\[ \text{Amount of milk in smaller jar} = \text{Total capacity} \times \text{Percentage of milk} \]
\[ = 3 \, \text{liters} \times \frac{25}{100} = 3 \times 0.25 = 0.75 \, \text{liters} \]

### Step 2: Calculate the amount of milk in the larger jar (5 liters).
The larger jar contains 25% water, which means it contains 75% milk. Therefore, the amount of milk in the larger jar can be calculated as follows:

\[ \text{Amount of milk in larger jar} = \text{Total capacity} \times \text{Percentage of milk} \]
\[ = 5 \, \text{liters} \times \frac{75}{100} = 5 \times 0.75 = 3.75 \, \text{liters} \]

### Step 3: Calculate the total amount of milk in the cask.
Now, we will add the amounts of milk from both jars to find the total amount of milk in the cask:

\[ \text{Total milk} = \text{Milk from smaller jar} + \text{Milk from larger jar} \]
\[ = 0.75 \, \text{liters} + 3.75 \, \text{liters} = 4.5 \, \text{liters} \]

### Step 4: Calculate the total volume of the mixture in the cask.
The total volume of the cask is 10 liters, and since we are combining the contents of both jars, we need to consider the total volume of liquid in the cask:

\[ \text{Total volume in cask} = 10 \, \text{liters} \]

### Step 5: Calculate the percentage of milk in the cask.
To find the percentage of milk in the cask, we will use the formula:

\[ \text{Percentage of milk} = \left( \frac{\text{Total milk}}{\text{Total volume in cask}} \right) \times 100 \]
\[ = \left( \frac{4.5 \, \text{liters}}{10 \, \text{liters}} \right) \times 100 = 45\% \]

### Final Answer:
The percentage of milk in the cask is **45%**.

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