Question

A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is

• A. 52%
• B. 50%
• C. 55%
• D. 48%

Answer 1

The Correct Option is B

To solve the problem, we need to determine the concentration of ethanol solution S.Let the volume of the 20% ethanol solution be V₁ and the volume of the unknown ethanol solution S be V₂. The problem states V₁ : V₂ = 1:3. Let’s assume V₁ = x and V₂ = 3x.

Now mix this with another equal volume of 20% ethanol solution:

Total volume specified for mixing the two ethanol solutions: (V₁ + V₂) + (V₁ + V₂) = 2(V₁ + V₂)

Ethanol from V₁: 0.2x

Ethanol from V₂: 0.01Sy (where S is the percentage of ethanol and as Volume V₂= 3x)

Ethanol from 2nd V₁: 0.2x
 

Solution	Volume	Ethanol Volume
First 20% solution	x	0.2x
Unknown solution S	3x	\(S \times 0.01 \times 3x\)
Second 20% Solution	4x	0.8x
Total	8x	\(0.2x + 0.01S \times 3x + 0.8x\)

According to the problem, the total ethanol in the final mixture = 31.25% of the total volume.Equating the ethanol in blended results:Total ethanol = \(0.2x + 0.01S \times 3x + 0.8x\) = 31.25% of \(8x\).

\(x(0.2 + 0.03S + 0.8) = 0.3125 \times 8x\) 

\(x(1 + 0.03S) = 2.5x\)

Dividing through by x and simplifying;
\(1 + 0.03S = 2.5\)
\(0.03S = 2.5 - 1\)
\(0.03S = 1.5\)
\(S = \frac{1.5}{0.03}\)
\(S = 50\)

The concentration of the unknown ethanol solution S is 50%.