In a mixture of milk and water of the volume of 60l the ratio of milk to water is 7:5. How much quantity of water will be added to make mixture of equal ratio?

Options

A. a. 8L
B. b. 10L
C. c. 15L
D. d. 20L

Answer

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

### Step 1: Understand the given information
We have a mixture of milk and water with a total volume of 60 liters. The ratio of milk to water is given as 7:5.

### Step 2: Calculate the total parts in the ratio
The total parts in the ratio of milk to water can be calculated as:
\[ 7 + 5 = 12 \]

### Step 3: Calculate the quantity of milk
To find the quantity of milk in the mixture, we use the formula:
\[ \text{Quantity of milk} = \frac{7}{12} \times 60 \]
Calculating this gives:
\[ \text{Quantity of milk} = \frac{7 \times 60}{12} = \frac{420}{12} = 35 \text{ liters} \]

### Step 4: Calculate the quantity of water
To find the quantity of water in the mixture, we use the formula:
\[ \text{Quantity of water} = \frac{5}{12} \times 60 \]
Calculating this gives:
\[ \text{Quantity of water} = \frac{5 \times 60}{12} = \frac{300}{12} = 25 \text{ liters} \]

### Step 5: Set up the equation for equal ratio
We need to find out how much water (let's call it \( x \)) we need to add to make the ratio of milk to water equal (1:1). After adding \( x \) liters of water, the new quantity of water will be:
\[ 25 + x \]
The quantity of milk remains the same at 35 liters. Therefore, we set up the equation:
\[ \frac{35}{25 + x} = 1 \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 35 = 25 + x \]

### Step 7: Solve for \( x \)
Rearranging the equation to isolate \( x \):
\[ x = 35 - 25 \]
Calculating this gives:
\[ x = 10 \]

### Conclusion
Thus, the quantity of water that needs to be added to make the mixture have an equal ratio of milk to water is **10 liters**.

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