3 litres of water is added to 15 litres of a mixture of a` 20%` solution of alcohol in water. The strength of alcohol is now…

Options

A. `12 1/2%`
B. `16 2/3%`
C. `24%`
D. `16%`

Answer

To find the new strength of alcohol in the mixture after adding water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the initial mixture and its alcohol content**:
- We have 15 litres of a mixture that contains 20% alcohol.
- To find the amount of alcohol in this mixture, we calculate:
\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} \]
\[ \text{Amount of alcohol} = 15 \, \text{litres} \times \frac{20}{100} = 3 \, \text{litres} \]

2. **Add water to the mixture**:
- We add 3 litres of water to the existing 15 litres of mixture.
- The new total volume of the mixture becomes:
\[ \text{New total volume} = 15 \, \text{litres} + 3 \, \text{litres} = 18 \, \text{litres} \]

3. **Calculate the new percentage of alcohol**:
- The amount of alcohol remains the same (3 litres) since we only added water.
- The new percentage of alcohol in the mixture is calculated as:
\[ \text{Percentage of alcohol} = \left(\frac{\text{Amount of alcohol}}{\text{New total volume}}\right) \times 100 \]
\[ \text{Percentage of alcohol} = \left(\frac{3 \, \text{litres}}{18 \, \text{litres}}\right) \times 100 = \frac{3}{18} \times 100 = \frac{1}{6} \times 100 \approx 16.67\% \]

4. **Convert the decimal to a fraction**:
- The percentage 16.67% can be expressed as \(16 \frac{2}{3}\%\) or \(16.67\%\).

### Final Answer:
The strength of alcohol in the new mixture is \(16 \frac{2}{3}\%\) or approximately \(16.67\%\).