A mixture contains alcohol and water in the ratio 4:3. if 7 liters of water is added to the mixture the ratio of alcohol and water becomes 3:4 . The quantity of alcohol in the mixture of

Options

A. 10 liters
B. 12 liters
C. 32 liters
D. 48 liters

Answer

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

### Step 1: Define the Variables
Let the quantity of alcohol in the mixture be \( 4x \) liters and the quantity of water be \( 3x \) liters, based on the initial ratio of alcohol to water (4:3).

### Step 2: Add Water
According to the problem, 7 liters of water is added to the mixture. Therefore, the new quantity of water becomes:
\[ 3x + 7 \text{ liters} \]

### Step 3: Set Up the New Ratio
After adding the water, the new ratio of alcohol to water is given as 3:4. We can set up the equation based on this new ratio:
\[ \frac{4x}{3x + 7} = \frac{3}{4} \]

### Step 4: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives us:
\[ 4 \cdot 4x = 3 \cdot (3x + 7) \]
This simplifies to:
\[ 16x = 9x + 21 \]

### Step 5: Solve for \( x \)
Subtract \( 9x \) from both sides:
\[ 16x - 9x = 21 \]
\[ 7x = 21 \]
Now, divide both sides by 7:
\[ x = 3 \]

### Step 6: Calculate the Quantity of Alcohol
Now that we have \( x \), we can find the quantity of alcohol:
\[ \text{Quantity of alcohol} = 4x = 4 \cdot 3 = 12 \text{ liters} \]

### Conclusion
The quantity of alcohol in the mixture is **12 liters**.

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