The concentration of spirit in three different vessels A, B and C are 45%, 30%…
2025
The concentration of spirit in three different vessels A, B and C are 45%, 30% and 25% respectively. If 4 liters from vessel A, 5 liters from vessel B and 6 liters from vessel C are mixed, find the concentration of spirit in the resultant solution.
- A.
35%
- B.
30%
- C.
32%
- D.
36%
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Correct answer: C
When solutions of different concentrations are mixed, the resultant concentration is not a simple average of the given percentages -- it is a volume-weighted average. Each vessel contributes an actual quantity of spirit equal to its volume multiplied by its own concentration; adding these quantities across all vessels and dividing by the total volume mixed gives the concentration of the resultant mixture.
Applying this to the three vessels:
Vessel A contributes 4 liters at 45% concentration, so its spirit quantity = 4 x 0.45 = 1.8 liters.
Vessel B contributes 5 liters at 30% concentration, so its spirit quantity = 5 x 0.30 = 1.5 liters.
Vessel C contributes 6 liters at 25% concentration, so its spirit quantity = 6 x 0.25 = 1.5 liters.
Total spirit in the mixture = 1.8 + 1.5 + 1.5 = 4.8 liters, and the total volume mixed = 4 + 5 + 6 = 15 liters.
Resultant concentration = (4.8 / 15) x 100 = 32%.
As a check, the same result follows directly from the percentage-weighted total without converting to liters of pure spirit first: (4 x 45 + 5 x 30 + 6 x 25) / (4 + 5 + 6) = 480 / 15 = 32%, confirming the answer.