Question

How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?

• A. 30
• B. 20
• C. 24
• D. 32

Answer 1

The Correct Option is B

To resolve the question of how many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to achieve a 50% alcohol solution, we'll apply the concept of mixture concentrations using algebra. 

1. Let the volume of the 30% alcohol solution to be added be x litres.
2. The total amount of alcohol in the 30% solution will be 0.3x litres.
3. The total alcohol in the existing 40 litres of 60% solution is 0.6 × 40 = 24 litres.
4. The total resulting volume of the solution will be x + 40 litres.
5. We want the final solution to have a 50% alcohol concentration. Therefore, the equation based on the total alcohol content is:

(0.3x+24)=0.5⁣(x+40)

1. Solving the equation step-by-step:

0.3x+24=0.5x+20

1. Rearrange to find x:

24-20=0.5x-0.3x

1. Simplify further:

4=0.2x

1. Divide both sides by 0.2 to solve for x:

x=40.2=20

1. Thus, 20 litres of the 30% alcohol solution should be added.