How many litres of water should be added to 24 litres of an acid and water solution, such that the concentration of acid in the solution decreases from 60% to 45%?

Sure, let's solve this step by step:

1. First, let's find out how much acid is in the original solution. Since the solution is 60% acid, that means 60% of the 24 litres is acid. So, 0.60 * 24 = 14.4 litres of the solution is acid.

2. Now, we want to add water to this solution to decrease the acid concentration to 45%. Let's denote the amount of water to be added as 'x' litres.

3. After adding the water, the total volume of the solution will be 24 + x litres. However, the amount of acid remains the same, which is 14.4 litres.

4. The new concentration of acid (45%) will be the amount of acid (14.4 litres) divided by the new total volume (24 + x litres). So, we can set up the equation: 14.4 / (24 + x) = 0.45

5. Solving this equation for 'x' will give us the amount of water that needs to be added.

6. Multiply both sides by (24 + x) to get rid of the denominator on the left side: 14.4 = 0.45 * (24 + x)

7. Distribute the 0.45 on the right side: 14.4 = 10.8 + 0.45x

8. Subtract 10.8 from both sides: 14.4 - 10.8 = 0.45x

9. Simplify the left side: 3.6 = 0.45x

10. Finally, divide both sides by 0.45 to solve for 'x': x = 3.6 / 0.45 = 8 litres

So, 8 litres of water should be added to the solution to decrease the acid concentration from 60% to 45%.