Four equal-volume vessels contain spirit concentrations of 60%, 70%, 75%, and 80%. If all are mixed in equal amounts, what is the ratio of spirit to water in the resulting mixture?

Introduction / Context:
When equal volumes are mixed, the final concentration is simply the arithmetic mean of the individual concentrations. Convert that to a spirit : water ratio by comparing to 100%.

Given Data / Assumptions:

• Spirit percentages: 60, 70, 75, 80.
• Equal volumes from each vessel.

Concept / Approach:
Average spirit% = (60 + 70 + 75 + 80)/4. Water% = 100 − spirit%. Ratio spirit : water = spirit% : water%.

Step-by-Step Solution:
Mean spirit% = 285/4 = 71.25%Water% = 100 − 71.25 = 28.75%Spirit : Water = 71.25 : 28.75 = (285 : 115) = 57 : 23

Verification / Alternative check:
Divide both by 5: 285 : 115 → 57 : 23; consistent.

Why Other Options Are Wrong:
57 : 13 and 23 : 57 imply impossible >100% or too little spirit; only 57 : 23 matches 71.25% spirit.

Common Pitfalls:
Taking a weighted average even though volumes are equal, or confusing spirit : water with water : spirit.

Final Answer:
57 : 23