15 litre of a mixture contains 20% alcohol and rest water. If 3 litre of water is added in it, then percentage of alcohol in the new mixture will be

Options

A. 0.25
B. 0.2
C. 0.1667
D. 0.3333

Answer

To solve the problem step by step, let's break it down:

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

\[ \text{Amount of alcohol} = \text{Total volume} \times \text{Percentage of alcohol} \]
\[ \text{Amount of alcohol} = 15 \, \text{liters} \times \frac{20}{100} = 15 \times 0.2 = 3 \, \text{liters} \]

### Step 2: Calculate the amount of water in the original mixture.
Since the mixture contains 20% alcohol, the rest is water.

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

### Step 3: Add 3 liters of water to the mixture.
Now, we add 3 liters of water to the original mixture.

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

### Step 4: Calculate the new total volume of the mixture.
The new total volume after adding the water is:

\[ \text{New total volume} = \text{Original volume} + \text{Added water} \]
\[ \text{New total volume} = 15 \, \text{liters} + 3 \, \text{liters} = 18 \, \text{liters} \]

### Step 5: Calculate the percentage of alcohol in the new mixture.
The amount of alcohol remains the same (3 liters), but the total volume has increased to 18 liters.

\[ \text{Percentage of alcohol in the new mixture} = \left( \frac{\text{Amount of alcohol}}{\text{New total volume}} \right) \times 100 \]
\[ \text{Percentage of alcohol in the new mixture} = \left( \frac{3 \, \text{liters}}{18 \, \text{liters}} \right) \times 100 = \frac{3}{18} \times 100 = \frac{1}{6} \times 100 \approx 16.67\% \]

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

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