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

Options

A. 12 litres
B. 16 litres
C. 7 litres
D. 10 litres

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the initial quantities of alcohol and water
Let the quantity of alcohol in the mixture be \( 4x \) liters and the quantity of water be \( 3x \) liters, where \( x \) is a common multiplier.

### Step 2: Set up the equation after adding water
When 7 liters of water is added to the mixture, the new quantity of water becomes:
\[ 3x + 7 \text{ liters} \]

### Step 3: Establish the new ratio
According to the problem, after adding 7 liters of water, the new ratio of alcohol to water becomes \( 3:4 \). Therefore, we can set up the following equation based on the new ratio:
\[ \frac{4x}{3x + 7} = \frac{3}{4} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 4 \cdot 4x = 3 \cdot (3x + 7) \]
This simplifies to:
\[ 16x = 9x + 21 \]

### Step 5: Solve for \( x \)
Now, we will isolate \( x \) by moving \( 9x \) to the left side:
\[ 16x - 9x = 21 \]
\[ 7x = 21 \]
Dividing both sides by 7 gives:
\[ x = 3 \]

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

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

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