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

Hint:

Write the alcohol content on both sides as an equation and solve for the added volume, or use the alligation rule.

Answer 1

The Correct Option is B

This same question can be solved faster using the rule of alligation, which directly compares how far each solution's strength is from the target strength.

1. The target concentration is 50%. The 30% solution is $50 - 30 = 20$ points below the target. The 60% solution is $60 - 50 = 10$ points above the target.
2. By the alligation rule, the two solutions mix in the ratio (distance of the other solution from the mean) : (distance of this solution from the mean), so the ratio of 30% solution to 60% solution is $10 : 20$, which simplifies to $1 : 2$.
3. This means for every 1 part of the 30% solution, there are 2 parts of the 60% solution.
4. The 60% solution's volume is fixed at 40 litres, and this represents the 2 parts in the ratio. So 1 part equals $\frac{40}{2} = 20$ litres.
5. Since the 30% solution is 1 part, its required volume is 20 litres.

Both the direct balance-equation method and the alligation ratio method agree on the same quantity.

\[\boxed{20 \text{ litres}}\]