Study the following information carefully and answer the given questions accordingly. Give answer
If ‘X’ litres was removed from a jar containing a mixture of milk and water in the ratio of `4:1` respectively, what is the value of X?
After removing 'X' litres of mixture from the jar, 16 litres of water was added, to the jar and the ratio of milk to water (in the jar) became `2:1`
‘X’ litres of the mixture constituted 20% of the original quantity of mixture in the jar.

Options

A. if the data in statement n alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
B. if the data either in statement I alone or in statement II alone are sufficient to answer the question
C. if the data in both the statements I and II together are not sufficient to answer the question
D. if the data in both the statements I and II together are necessary to answer the question

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the initial conditions
We have a jar containing a mixture of milk and water in the ratio of 4:1. Let's denote the initial quantities of milk and water as follows:
- Milk = 4A
- Water = A

### Step 2: Calculate the total initial quantity of the mixture
The total quantity of the mixture in the jar can be calculated as:
\[ \text{Total mixture} = \text{Milk} + \text{Water} = 4A + A = 5A \]

### Step 3: Determine the amount removed
Let 'X' litres be the amount of mixture removed from the jar. According to the problem, X litres constitutes 20% of the original quantity of the mixture:
\[ X = 0.2 \times (5A) = A \]

### Step 4: Calculate the quantities of milk and water removed
Since the mixture is in the ratio of 4:1, when X litres is removed:
- Milk removed = \( \frac{4}{5}X = \frac{4}{5}A \)
- Water removed = \( \frac{1}{5}X = \frac{1}{5}A \)

### Step 5: Calculate the remaining quantities after removal
After removing X litres from the jar, the remaining quantities of milk and water will be:
- Remaining milk = \( 4A - \frac{4}{5}A = \frac{16}{5}A \)
- Remaining water = \( A - \frac{1}{5}A = \frac{4}{5}A \)

### Step 6: Add water to the jar
Next, 16 litres of water is added to the jar. The new quantity of water will be:
\[ \text{New water quantity} = \frac{4}{5}A + 16 \]

### Step 7: Set up the ratio of milk to water
According to the problem, after adding the water, the ratio of milk to water becomes 2:1. Therefore, we can set up the equation:
\[ \frac{\text{Remaining milk}}{\text{New water quantity}} = \frac{2}{1} \]
Substituting the values we have:
\[ \frac{\frac{16}{5}A}{\frac{4}{5}A + 16} = 2 \]

### Step 8: Solve the equation
Cross-multiplying gives:
\[ \frac{16}{5}A = 2 \left(\frac{4}{5}A + 16\right) \]
Expanding the right side:
\[ \frac{16}{5}A = \frac{8}{5}A + 32 \]
Bringing all terms involving A to one side:
\[ \frac{16}{5}A - \frac{8}{5}A = 32 \]
This simplifies to:
\[ \frac{8}{5}A = 32 \]
Multiplying both sides by \( \frac{5}{8} \):
\[ A = 20 \]

### Step 9: Calculate the value of X
Since we previously established that \( X = A \), we find:
\[ X = 20 \text{ litres} \]

### Final Answer
The value of X is **20 litres**.

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