Two litres of pure alcohol are added to 6 litres of a solution that contains 40% alcohol and 60% water. After mixing, what is the percentage of water in the final 8 litre solution?

Introduction / Context:

This problem belongs to the topic of mixtures and alligation, framed here using percentages. It tests your ability to separate components of a solution, add another component, and then recompute the percentage of one constituent, in this case water. Such mixture questions appear frequently in quantitative aptitude exams.

Given Data / Assumptions:

• Initial solution volume = 6 litres.
• Initial solution has 40% alcohol and 60% water.
• Pure alcohol added = 2 litres.
• Total final volume after mixing = 6 + 2 = 8 litres.
• We need the percentage of water in the final solution.

Concept / Approach:

The key approach is to separately track the quantities of alcohol and water. In the original solution, the water and alcohol amounts can be found using their percentages. When pure alcohol is added, only the alcohol quantity increases, while water stays the same. After finding the new total volumes of alcohol and water, we compute the new water percentage as (water volume / total volume) * 100.

Step-by-Step Solution:

Verification / Alternative check:

We can cross-check arithmetic: 3.6 divided by 8 equals 0.45. Multiplying by 100 gives 45%. Also, the alcohol percentage would be 55%, because 4.4 / 8 = 0.55, and 45% + 55% = 100%. This consistency check confirms that the water percentage is correctly calculated.

Why Other Options Are Wrong:

• 55%: This is actually the alcohol percentage, not the water percentage, in the final mixture.
• 60% and 65%: These values would imply that the water portion increased or did not change, which is impossible because additional alcohol was added but no extra water was added.
• 50%: This would correspond to equal quantities of water and alcohol, which does not match the computed values.

Common Pitfalls:

One common mistake is to take the average of 40% and some assumed higher value without considering volumes. Another error is to forget that water quantity stays constant when pure alcohol is added. Some students incorrectly assume that the original 60% water remains 60% in the final solution. Always recompute based on actual quantities rather than relying on mental shortcuts.

Final Answer:

The percentage of water in the final solution is 45%.