In a mixture of 50 litres, milk and water are in the ratio of 3:2. How much water should be added to make the ratio of the two equal?

Options

A. 20 litres
B. 14 litres
C. 10 litres
D. 15 litres

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript:

### Step 1: Understand the given information
We have a mixture of 50 liters of milk and water in the ratio of 3:2.

### Step 2: Determine the total parts in the ratio
The total parts in the ratio of milk to water (3:2) is:
\[ 3 + 2 = 5 \text{ parts} \]

### Step 3: Calculate the quantity of milk and water
Now, we can find the quantity of milk and water in the mixture:
- Quantity of milk:
\[ \text{Milk} = \left(\frac{3}{5}\right) \times 50 = 30 \text{ liters} \]
- Quantity of water:
\[ \text{Water} = \left(\frac{2}{5}\right) \times 50 = 20 \text{ liters} \]

### Step 4: Set up the equation to find the amount of water to be added
We need to add water to make the ratio of milk to water equal (1:1). Since we are keeping the quantity of milk constant at 30 liters, we need to find out how much water (let's call it \( x \)) we need to add to the existing 20 liters of water to make the total amount of water equal to the amount of milk:
\[ 30 = 20 + x \]

### Step 5: Solve for \( x \)
Rearranging the equation gives us:
\[ x = 30 - 20 = 10 \text{ liters} \]

### Conclusion
Therefore, the amount of water that should be added to make the ratio of milk and water equal is **10 liters**.

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