How many litres 3% alcohol solution should be mixed with a 6 litres of 30% alcohol solution so as to get a 12% solution?
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Let the solution with 3% alcohol concentration be x litres
The amount of alcohol is :
0.03x litres
From the 6 litres the amount of alcohol is :
30/100 × 6 = 1.8 litres
The new solution will have :
(0.03x + 1.8) litres of alcohol.
This is 12% of the total solution.
The total solution is :
(x + 6) litres
12% of this is :
0.12 × (x + 6) = 0.12x + 0.72
0.12x + 0.72 = 0.03x + 1.8
0.12x - 0.03x = 1.8 - 0.72
0.09x = 1.08
x = 12
The answer is 12 litres
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