Three different mixtures contain glucose and alcohol with glucose concentrations of 12%, 35%, and 45% respectively. If 2 litres from the first vessel, 3 litres from the second vessel, and 1 litre from the third vessel are mixed together, what will be the ratio of glucose to alcohol in the new mixture?

Introduction / Context:
This problem tests mixture composition using weighted averages. When you combine liquids from multiple sources with different percentages, the correct way is to compute the absolute amount of the ingredient (glucose) contributed by each portion, sum them, and then compare with the remaining part (alcohol). The final ratio is based on total glucose and total alcohol in the combined volume.

Given Data / Assumptions:

• Vessel 1 glucose = 12%
• Vessel 2 glucose = 35%
• Vessel 3 glucose = 45%
• Volumes mixed: 2 L, 3 L, 1 L respectively
• Each mixture contains only glucose and alcohol

Concept / Approach:
Glucose amount = (percentage/100) * volume. Alcohol amount = total volume - total glucose. Then form the ratio glucose:alcohol and simplify.

Step-by-Step Solution:

Verification / Alternative check:
Glucose fraction in final mix = 1.74/6 = 0.29 = 29%. Alcohol fraction = 71%. Ratio 29:71 is consistent with the computed percentage split.

Why Other Options Are Wrong:

Common Pitfalls:
A common mistake is to average the percentages directly: (12 + 35 + 45)/3, which ignores unequal volumes. Always weight by volume. Another mistake is to forget to compute alcohol as the remainder after total glucose is found.

Final Answer:
29:71