A mixture contains alcohol and water in the ratio of 12 : 5. On adding 14 liters of water, the ratio of alcohol to water becomes 4 : 3. The quantity of alcohol in the mixture is:

The correct answer is 42 L.

Step-by-step Explanation:

Step 1: Define initial quantities using a variable.
Let the initial ratio of alcohol to water be $12:5$.
Let the quantity of alcohol in the mixture be $12x$ liters and the quantity of water be $5x$ liters.

Step 2: Formulate the equation after adding water.
When 14 liters of water are added to the mixture, the new quantity of water becomes $(5x+14)$ liters.
The quantity of alcohol remains unchanged at $12x$ liters.

The new ratio of alcohol to water is given as $4:3$. Therefore, we can set up the equation:

$\frac{12x}{5x+14}=\frac{4}{3}$

Step 3: Solve for $x$.
Cross-multiplying the terms gives:

$12x\times 3=4\times (5x+14)$

$36x=20x+56$

Subtracting $20x$ from both sides:

$36x-20x=56$

$16x=56$

$x=\frac{56}{16}=3.5$

Step 4: Find the quantity of alcohol.
The initial quantity of alcohol is $12x$.

$\text{Quantity of alcohol}=12\times 3.5=42\text{liters}$

Thus, the quantity of alcohol in the mixture is 42 L.