In a 56 liters mixture of milk and water , the ratio of milk to water is 5:2 . In order to make the ratio of milk to water 7: 2, some quantity of milk is to be added to the mixture. The quanity of the milk is to be added to the mixture . The quantity of the milk present in the new mixture will be :

Options

A. 40 liters
B. 16 lites
C. 56 liters
D. 48 lites

Answer

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

### Step 1: Determine the initial quantities of milk and water
The total volume of the mixture is 56 liters, and the ratio of milk to water is 5:2.

Let the quantity of milk be \(5x\) and the quantity of water be \(2x\).

The total mixture can be expressed as:
\[ 5x + 2x = 56 \]
\[ 7x = 56 \]
\[ x = \frac{56}{7} = 8 \]

Now, we can find the quantities of milk and water:
- Quantity of milk:
\[ 5x = 5 \times 8 = 40 \text{ liters} \]
- Quantity of water:
\[ 2x = 2 \times 8 = 16 \text{ liters} \]

### Step 2: Set up the new ratio of milk to water
We want to change the ratio of milk to water to 7:2. The quantity of water remains the same (16 liters), and we need to find out how much milk should be added.

Let the quantity of milk to be added be \(y\). The new quantity of milk will then be:
\[ 40 + y \]

### Step 3: Set up the equation for the new ratio
The new ratio of milk to water can be expressed as:
\[ \frac{40 + y}{16} = \frac{7}{2} \]

### Step 4: Cross-multiply to solve for \(y\)
Cross-multiplying gives:
\[ 2(40 + y) = 7 \times 16 \]
\[ 80 + 2y = 112 \]
\[ 2y = 112 - 80 \]
\[ 2y = 32 \]
\[ y = \frac{32}{2} = 16 \]

### Step 5: Calculate the new quantity of milk
Now that we know the quantity of milk to be added is 16 liters, we can find the total quantity of milk in the new mixture:
\[ \text{New quantity of milk} = 40 + 16 = 56 \text{ liters} \]

### Final Answer
The quantity of milk present in the new mixture will be **56 liters**.

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