A quantity of 30 ml of 20% alcohol is mixed with 20 ml of 25% alcohol. What is the strength of alcohol in the mixture ?

Answer

To find the strength of alcohol in the mixture of two solutions, we will follow these steps:

### Step 1: Calculate the amount of alcohol in the first solution (30 ml of 20% alcohol)
- The amount of alcohol can be calculated using the formula:
\[ \text{Amount of alcohol} = \text{Percentage} \times \text{Total volume} \]
- For the first solution:
\[ \text{Amount of alcohol} = \frac{20}{100} \times 30 = 6 \text{ ml} \]

### Step 2: Calculate the amount of alcohol in the second solution (20 ml of 25% alcohol)
- Using the same formula:
\[ \text{Amount of alcohol} = \frac{25}{100} \times 20 = 5 \text{ ml} \]

### Step 3: Calculate the total amount of alcohol in the mixture
- Add the amounts of alcohol from both solutions:
\[ \text{Total alcohol} = 6 \text{ ml} + 5 \text{ ml} = 11 \text{ ml} \]

### Step 4: Calculate the total volume of the mixture
- The total volume is the sum of the volumes of both solutions:
\[ \text{Total volume} = 30 \text{ ml} + 20 \text{ ml} = 50 \text{ ml} \]

### Step 5: Calculate the strength of alcohol in the mixture
- The strength (percentage) of alcohol in the mixture can be calculated using the formula:
\[ \text{Percentage of alcohol} = \left( \frac{\text{Total alcohol}}{\text{Total volume}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of alcohol} = \left( \frac{11 \text{ ml}}{50 \text{ ml}} \right) \times 100 = 22\% \]

### Final Answer
The strength of alcohol in the mixture is **22%**.

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