A 12 litre solution of acid and water contains 30% acid. How much water (in litres) must be added to get a solution having 20% acid?

The correct answer is 6.

Step-by-Step Explanation:

1. Find the amount of acid in the original solution:

The initial volume of the solution is 12 litres, and it contains 30% acid.

$\text{Amount of acid}=30\%\text{of}12$

$\text{Amount of acid}=\frac{30}{100}\times 12=3.6\text{litres}$

2. Set up the equation for the new solution:

Let $x$ be the amount of water (in litres) added to the solution.

When only water is added, the total amount of acid remains unchanged at 3.6 litres.

The new total volume of the solution becomes $(12+x)$ litres.

We want the new solution to contain 20% acid. Therefore, the ratio of acid to the new total volume must equal 20%:

$\frac{3.6}{12+x}=20\%$

$\frac{3.6}{12+x}=\frac{20}{100}=\frac{1}{5}$

3. Solve for $x$:

Cross-multiplying gives:

$3.6\times 5=12+x$

$18=12+x$

$x=18-12$

$x=6$

Thus, 6 litres of water must be added to get a solution having 20% acid.