In a mixture of 120 litres, the ratio of milk and water is 2:1. If the ratio of milk and water is 1:2, then the amount of water (in litres) is required to be added is:

Options

A. 20
B. 40
C. 80
D. 120

Answer

To solve the problem step by step, we need to determine how much water needs to be added to change the ratio of milk and water from 2:1 to 1:2 in a mixture of 120 liters.

### Step 1: Understand the initial ratio of milk and water
The initial ratio of milk to water is given as 2:1. This means for every 2 parts of milk, there is 1 part of water.

### Step 2: Calculate the total parts in the initial mixture
The total parts in the initial mixture can be calculated as:
- Milk parts = 2
- Water parts = 1
- Total parts = 2 + 1 = 3

### Step 3: Determine the quantity of milk and water in the initial mixture
Since the total volume of the mixture is 120 liters, we can find the quantity of milk and water:
- Quantity of 1 part = Total volume / Total parts = 120 liters / 3 = 40 liters
- Quantity of milk = 2 parts = 2 * 40 liters = 80 liters
- Quantity of water = 1 part = 1 * 40 liters = 40 liters

### Step 4: Understand the final desired ratio of milk and water
The final desired ratio of milk to water is 1:2. This means for every 1 part of milk, there are 2 parts of water.

### Step 5: Calculate the total parts in the final mixture
For the final ratio of 1:2:
- Milk parts = 1
- Water parts = 2
- Total parts = 1 + 2 = 3

### Step 6: Set up the equation for the final mixture
Let \( x \) be the amount of water to be added. The quantity of milk remains the same (80 liters), and the quantity of water will be the initial water plus the added water:
- Final quantity of water = Initial water + Added water = 40 liters + \( x \)

### Step 7: Set up the ratio equation based on the final ratio
According to the final ratio:
\[ \frac{\text{Milk}}{\text{Water}} = \frac{1}{2} \]
Substituting the values:
\[ \frac{80}{40 + x} = \frac{1}{2} \]

### Step 8: Solve the equation
Cross-multiplying gives:
\[ 80 * 2 = 1 * (40 + x) \]
\[ 160 = 40 + x \]
Subtracting 40 from both sides:
\[ x = 160 - 40 \]
\[ x = 120 \]

### Conclusion
The amount of water required to be added is **120 liters**.

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