The ratio of milk and water in a pot is 5:7. If we add 5l milk and 5 l water then ratio becomes 3: 4. Find the initial quantity of milk.

Options

A. 5 litre
B. 10 litre
C. 25 litre
D. 15 litre

Answer

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

### Step 1: Understand the initial ratio of milk and water
The initial ratio of milk to water is given as 5:7. This means that for every 5 parts of milk, there are 7 parts of water.

### Step 2: Define variables for the initial quantities
Let the initial quantity of milk be \(5k\) liters and the initial quantity of water be \(7k\) liters, where \(k\) is a common multiplier.

### Step 3: Set up the equation after adding milk and water
When we add 5 liters of milk and 5 liters of water, the new quantities become:
- Milk: \(5k + 5\) liters
- Water: \(7k + 5\) liters

The new ratio of milk to water is given as 3:4. We can express this as:
\[ \frac{5k + 5}{7k + 5} = \frac{3}{4} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 4(5k + 5) = 3(7k + 5) \]

### Step 5: Expand both sides of the equation
Expanding both sides, we have:
\[ 20k + 20 = 21k + 15 \]

### Step 6: Rearrange the equation to solve for \(k\)
Rearranging the equation, we can isolate \(k\):
\[ 20k + 20 - 15 = 21k \]
\[ 20k + 5 = 21k \]
\[ 21k - 20k = 5 \]
\[ k = 5 \]

### Step 7: Calculate the initial quantity of milk
Now that we have \(k\), we can find the initial quantity of milk:
\[ \text{Initial quantity of milk} = 5k = 5 \times 5 = 25 \text{ liters} \]

### Final Answer
The initial quantity of milk is **25 liters**.

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