The ratio of milk and water in a pot in 2 : 3. If we subtracted 3l water then ratio become 5: 7. Find the initial quantity of milk.

Options

A. 30 litre
B. 15 litre
C. 35 litre
D. 10 litre

Answer

To solve the problem step by step, we will use the information given about the ratios of milk and water.

### Step-by-Step Solution:

1. **Define Variables:**
Let the initial quantities of milk and water be represented in terms of a common variable \( k \).
- Milk = \( 2k \)
- Water = \( 3k \)

2. **Set Up the Equation After Removing Water:**
When 3 liters of water is subtracted, the new quantity of water becomes:
- New Water = \( 3k - 3 \)

According to the problem, the new ratio of milk to water becomes \( 5:7 \). Therefore, we can set up the equation:
\[ \frac{2k}{3k - 3} = \frac{5}{7} \]

3. **Cross Multiply to Solve for \( k \):**
Cross multiplying gives us:
\[ 2k \cdot 7 = 5 \cdot (3k - 3) \]
Simplifying this, we get:
\[ 14k = 15k - 15 \]

4. **Rearrange the Equation:**
Rearranging the equation to isolate \( k \):
\[ 14k - 15k = -15 \]
\[ -k = -15 \]
\[ k = 15 \]

5. **Calculate the Initial Quantity of Milk:**
Now that we have the value of \( k \), we can find the initial quantity of milk:
\[ \text{Initial quantity of milk} = 2k = 2 \times 15 = 30 \text{ liters} \]

### Final Answer:
The initial quantity of milk is **30 liters**.

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