15 litres of mixture contains 20% alcohol and the rest of water. If 3 litres of water be mixed with it, the percentage of alcohol in the new mixture would be :

Options

A. `15%`
B. `16 2/3%`
C. `17%`
D. `18 1/2 %`

Answer

To solve the problem step by step, follow these instructions:

### Step 1: Calculate the amount of alcohol in the original mixture.
The original mixture is 15 litres and contains 20% alcohol.

\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} \]
\[ \text{Amount of alcohol} = 15 \, \text{litres} \times \frac{20}{100} = 3 \, \text{litres} \]

### Step 2: Calculate the amount of water in the original mixture.
Since the rest of the mixture is water, we can find the amount of water by subtracting the amount of alcohol from the total volume.

\[ \text{Amount of water} = \text{Total volume} - \text{Amount of alcohol} \]
\[ \text{Amount of water} = 15 \, \text{litres} - 3 \, \text{litres} = 12 \, \text{litres} \]

### Step 3: Add the additional water to the mixture.
We are adding 3 litres of water to the original mixture.

\[ \text{New amount of water} = \text{Original amount of water} + \text{Added water} \]
\[ \text{New amount of water} = 12 \, \text{litres} + 3 \, \text{litres} = 15 \, \text{litres} \]

### Step 4: Calculate the total volume of the new mixture.
The total volume of the new mixture is the sum of the original mixture and the added water.

\[ \text{Total volume of new mixture} = \text{Original mixture} + \text{Added water} \]
\[ \text{Total volume of new mixture} = 15 \, \text{litres} + 3 \, \text{litres} = 18 \, \text{litres} \]

### Step 5: Calculate the percentage of alcohol in the new mixture.
Now we can find the percentage of alcohol in the new mixture using the formula:

\[ \text{Percentage of alcohol} = \left( \frac{\text{Amount of alcohol}}{\text{Total volume of new mixture}} \right) \times 100 \]
\[ \text{Percentage of alcohol} = \left( \frac{3 \, \text{litres}}{18 \, \text{litres}} \right) \times 100 = 16.67\% \]

### Conclusion:
The percentage of alcohol in the new mixture is approximately **16.67%**.

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