A mixture contains acid and water in the ratio of 6 : 1. On adding 12 litres of water to the mixture, the ratio of acid to water becomes 3:2. The quantity of water (in litres) in the original mixture was:

Options

A. 3.5
B. 6
C. 4
D. 5

Answer

To solve the problem, we need to find out how much water was in the original mixture given the ratios and the additional water added. Let's break it down step by step.

### Step-by-Step Solution:

1. **Define Variables**:
Let the quantity of acid in the original mixture be \(6k\) litres and the quantity of water be \(k\) litres. The ratio of acid to water is given as 6:1.

2. **Add Water**:
After adding 12 litres of water, the new quantity of water becomes \(k + 12\) litres.

3. **Set Up the New Ratio**:
After adding the water, the ratio of acid to water becomes 3:2. Therefore, we can set up the equation:
\[ \frac{6k}{k + 12} = \frac{3}{2} \]

4. **Cross Multiply**:
To eliminate the fraction, we cross multiply:
\[ 6k \cdot 2 = 3 \cdot (k + 12) \]
This simplifies to:
\[ 12k = 3k + 36 \]

5. **Rearrange the Equation**:
Now, we rearrange the equation to isolate \(k\):
\[ 12k - 3k = 36 \]
This simplifies to:
\[ 9k = 36 \]

6. **Solve for \(k\)**:
Now, divide both sides by 9:
\[ k = \frac{36}{9} = 4 \]

7. **Find the Quantity of Water**:
The quantity of water in the original mixture is \(k\) litres. Since \(k = 4\), the quantity of water is:
\[ \text{Water in original mixture} = k = 4 \text{ litres} \]

### Final Answer:
The quantity of water in the original mixture was **4 litres**.

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