In a mixture 25 litres, the ratio of milk and water is `4:1`. How many litres of milk must be added to make to ratio `16:1`?
A. 21
B. 25
C. 60
D. 36

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem step by step, we will analyze the given information and perform the necessary calculations.

### Step 1: Understand the initial ratio and total volume
We are given a mixture of 25 liters where the ratio of milk to water is 4:1. This means that for every 4 parts of milk, there is 1 part of water.

**Hint:** Identify the total number of parts in the ratio.

### Step 2: Calculate the total parts in the initial ratio
The total parts in the ratio of milk to water (4:1) is:
\[ 4 + 1 = 5 \text{ parts} \]

**Hint:** Add the parts of the ratio to find the total parts.

### Step 3: Determine the volume of milk and water
Now, we can find the volume of milk and water in the mixture:
- Volume of milk:
\[ \text{Volume of milk} = \left(\frac{4}{5}\right) \times 25 = 20 \text{ liters} \]
- Volume of water:
\[ \text{Volume of water} = \left(\frac{1}{5}\right) \times 25 = 5 \text{ liters} \]

**Hint:** Use the ratio to calculate the individual volumes based on the total volume.

### Step 4: Set up the new ratio after adding milk
We want to change the ratio of milk to water to 16:1. After adding \( x \) liters of milk, the new volume of milk will be:
\[ 20 + x \text{ liters} \]
The volume of water remains the same at 5 liters.

**Hint:** Express the new volumes in terms of the variable \( x \).

### Step 5: Write the equation for the new ratio
We set up the equation for the new ratio:
\[ \frac{20 + x}{5} = 16 \]

**Hint:** Set up the equation based on the desired ratio.

### Step 6: Solve for \( x \)
Cross-multiply to solve for \( x \):
\[ 20 + x = 16 \times 5 \]
\[ 20 + x = 80 \]
Subtract 20 from both sides:
\[ x = 80 - 20 \]
\[ x = 60 \]

**Hint:** Isolate \( x \) to find how much milk needs to be added.

### Conclusion
To achieve the desired ratio of 16:1, we need to add **60 liters of milk**.

**Final Answer:** C. 60