In the 75 litres of mixture of milk and water, the ratio of milk and water is 4 : 1. the quantity of water required to make the ratio of milk and water 3 : 1 is :

Options

A. 1 litre
B. 3 litres
C. 4 litres
D. 5 litres

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the initial mixture
We have a mixture of milk and water, where the total volume is 75 liters and the ratio of milk to water is 4:1.

**Hint:** Identify the total parts in the ratio to find the individual quantities of milk and water.

### Step 2: Calculate the total parts in the ratio
The ratio of milk to water is 4:1, which means there are a total of \(4 + 1 = 5\) parts.

**Hint:** Remember that the total parts in a ratio are the sum of the individual 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 = \(\frac{4}{5} \times 75\) liters
- Quantity of water = \(\frac{1}{5} \times 75\) liters

Calculating these:
- Quantity of milk = \(60\) liters
- Quantity of water = \(15\) liters

**Hint:** Use the formula \(\text{Quantity} = \frac{\text{Part}}{\text{Total Parts}} \times \text{Total Volume}\) to find individual quantities.

### Step 4: Set up the new ratio
We need to change the ratio of milk to water from 4:1 to 3:1. This means that for every 3 parts of milk, there should be 1 part of water.

**Hint:** Write down the new ratio and express it in terms of parts.

### Step 5: Equalize the quantity of milk
Since the quantity of milk remains the same, we will keep it at 60 liters. In the new ratio of 3:1, if the quantity of milk is 3 parts, we can express it as:
- Let the new quantity of water be \(x\) liters.

From the ratio, we have:
\[ \frac{60}{x} = \frac{3}{1} \]

**Hint:** Set up a proportion based on the new ratio.

### Step 6: Solve for the new quantity of water
Cross-multiplying gives us:
\[ 60 = 3x \implies x = \frac{60}{3} = 20 \text{ liters} \]

**Hint:** Isolate the variable to find the new quantity of water.

### Step 7: Calculate the additional water required
We initially had 15 liters of water, and now we need 20 liters. Therefore, the additional water required is:
\[ \text{Additional water} = 20 - 15 = 5 \text{ liters} \]

**Hint:** Subtract the initial quantity from the new quantity to find how much more is needed.

### Final Answer
The quantity of water required to make the ratio of milk and water 3:1 is **5 liters**.

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