A 400 mL solution is `20%` alcohol by volume. If 100 mL of water is added, what the new concentration of alcohol, as a percent of volume?

Options

A. `5%`
B. `10%`
C. `12%`
D. `16%`

Answer

To solve the problem step by step, we will follow the process of calculating the concentration of alcohol in the solution after adding water.

### Step 1: Calculate the amount of alcohol in the original solution
Given that the original solution is 400 mL and is 20% alcohol by volume, we can calculate the volume of alcohol as follows:

\[ \text{Volume of alcohol} = \frac{20}{100} \times 400 = 80 \text{ mL} \]

### Step 2: Determine the new total volume after adding water
When we add 100 mL of water to the original solution, the new total volume becomes:

\[ \text{New total volume} = 400 \text{ mL} + 100 \text{ mL} = 500 \text{ mL} \]

### Step 3: Calculate the new concentration of alcohol
The concentration of alcohol is now calculated as the volume of alcohol divided by the new total volume, multiplied by 100 to convert it into a percentage:

\[ \text{New concentration of alcohol} = \left( \frac{80 \text{ mL}}{500 \text{ mL}} \right) \times 100 \]

Calculating this gives:

\[ \text{New concentration of alcohol} = \left( \frac{80}{500} \right) \times 100 = 16\% \]

### Conclusion
The new concentration of alcohol in the solution after adding 100 mL of water is **16%**.

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