A mixture contains milk and water in the ratio 5:1. On adding 5 litres of water, the ratio of milk to water becomes 5:2. The quantity of milk in the original mixture is

Options

A. 16 litres
B. 22.75 litres
C. 25 litres
D. 32.5 litres

Answer

To find the quantity of milk in the original mixture, we can follow these steps:

### Step 1: Define the quantities of milk and water
Let the quantity of milk in the original mixture be \(5x\) and the quantity of water be \(x\). This is based on the given ratio of milk to water, which is \(5:1\).

### Step 2: Set up the new quantity of water
According to the problem, when we add 5 liters of water, the new quantity of water becomes \(x + 5\).

### Step 3: Set up the new ratio
After adding 5 liters of water, the ratio of milk to water becomes \(5:2\). This means we can set up the equation:
\[ \frac{5x}{x + 5} = \frac{5}{2} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 5 \cdot (x + 5) = 2 \cdot 5x \]
This simplifies to:
\[ 5x + 25 = 10x \]

### Step 5: Rearrange the equation
Now, rearranging the equation to isolate \(x\):
\[ 25 = 10x - 5x \]
This simplifies to:
\[ 25 = 5x \]

### Step 6: Solve for \(x\)
Dividing both sides by 5 gives:
\[ x = 5 \]

### Step 7: Find the quantity of milk
Now, we can find the quantity of milk in the original mixture:
\[ \text{Quantity of milk} = 5x = 5 \cdot 5 = 25 \text{ liters} \]

### Final Answer
The quantity of milk in the original mixture is **25 liters**.

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