Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

The correct option is 92%.

Let us break down the problem step-by-step to find the percentage of alcohol in solution B.

Step 1: Understand the initial mixture
Let the volumes of alcohol solutions A and B mixed initially be in the ratio 1:3.
To make calculations easy, let us assume we mix:
Volume of solution A = $x$ liters
Volume of solution B = $3x$ liters
The total volume of this initial mixture is: $$V_{\text{initial}}=x+3x=4x$$

Step 2: Double the volume by adding solution A
The volume of the mixture is doubled by adding more of solution A. Since the initial volume is $4x$ , doubling it means the new total volume becomes $8x$ .
The volume of solution A added to double the mixture is: $$V_{\text{added A}}=8x-4x=4x$$

Thus, in the final mixture of volume $8x$ , the components are:
Total volume of solution A = Initial volume of A + Added volume of A = $x+4x=5x$
Total volume of solution B = $3x$

Step 3: Set up the alcohol concentration equation
We are given:
Alcohol concentration in solution A = 60% = 0.60
Let the alcohol concentration in solution B be $b\%$ (or $\frac{b}{100}$ as a fraction).
The resulting mixture has 72% alcohol.

The total volume of pure alcohol in the final mixture is the sum of alcohol from solution A and solution B:
Alcohol from A = $60\%\text{of}5x=0.60\times 5x=3x$
Alcohol from B = $b\%\text{of}3x=\frac{b}{100}\times 3x$

The total alcohol in the final mixture of volume $8x$ is 72%:
Total Alcohol = $72\%\text{of}8x=0.72\times 8x=5.76x$

Now, we equate the sum of individual alcohol contents to the total alcohol content: $$3x+\frac{3b}{100}x=5.76x$$

Dividing the entire equation by $x$ (since $x\ne 0$ ): $$3+\frac{3b}{100}=5.76$$

Subtract 3 from both sides: $$\frac{3b}{100}=2.76$$

Multiply by 100: $$3b=276$$

Divide by 3: $$b=92$$

Therefore, the percentage of alcohol in solution B is 92%.