In a mixture of 60 litres the ratio of milk and water is 2:1 what amount of water must be added to make the ratio 1:2?

Options

A. 42 litres
B. 56 litres
C. 60 litres
D. 77 litres

Answer

To solve the problem step by step, we will first determine the quantities of milk and water in the initial mixture, and then we will find out how much water needs to be added to achieve the desired ratio.

### Step 1: Determine the initial quantities of milk and water.
Given the total volume of the mixture is 60 liters and the ratio of milk to water is 2:1.

- The total parts in the ratio = 2 (milk) + 1 (water) = 3 parts.
- Quantity of milk = (2/3) * 60 L = 40 L.
- Quantity of water = (1/3) * 60 L = 20 L.

### Step 2: Set up the equation for the new ratio.
We want to change the ratio of milk to water from 2:1 to 1:2.

Let the amount of water to be added be \( x \) liters.

After adding \( x \) liters of water, the new quantity of water will be:
- New quantity of water = 20 L + \( x \) L.

### Step 3: Write the equation based on the new ratio.
We want the new ratio of milk to water to be 1:2.

This can be expressed as:
\[ \frac{\text{Quantity of Milk}}{\text{Quantity of Water}} = \frac{1}{2} \]
Substituting the known quantities:
\[ \frac{40}{20 + x} = \frac{1}{2} \]

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives:
\[ 40 \cdot 2 = 1 \cdot (20 + x) \]
\[ 80 = 20 + x \]

### Step 5: Solve for \( x \).
Subtract 20 from both sides:
\[ 80 - 20 = x \]
\[ x = 60 \]

### Conclusion:
The amount of water that must be added to make the ratio of milk to water 1:2 is **60 liters**.

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