Question

37.85% and 92% alcoholic solutions are mixed to get 35 litres of an 89% alcoholic solution. How many litres of each solution are there in the new mixture?

• A. 1.94 of the first and 33.06 of the second
• B. 20 of the first and 15 of the second
• C. 15 of the first and 20 of the second
• D. 12 of the first and 23 of the second

Answer 1

The Correct Option is A

Let \(x\) and \((35-x)\) litres of each solution be mixed.
\(37.85\%\) of \(x+92\%\) of (\(35-x\))=\(89\%\) of \(35\)
\(37.85x+92(35−x)=89×35\)
\(37.85x−92x=(89×35)−(92×35)\)
\(54.15x=35×3=105\)
\(x=\frac{105}{54.15}\approx1.94\)
Therefore, 1.94 litres of the first and 33.06 litres of the second
The correct answer is (A) : 1.94 of the first and 33.06 of the second