In one litre of a mixture of alcohol and water, water is 30%. The amount of alcohol that must be added to the mixture so that the part of water in the mixture be comes 15% is

Options

A. 1000ml
B. 700ml
C. 300ml
D. 900ml

Answer

To solve the problem step by step, we need to find out how much alcohol must be added to a 1-liter mixture of alcohol and water, where water constitutes 30% of the mixture, in order to reduce the percentage of water to 15%.

### Step-by-Step Solution:

1. **Identify the initial quantities**:
- The total volume of the mixture = 1 liter = 1000 ml.
- Water in the mixture = 30% of 1000 ml = 0.30 * 1000 ml = 300 ml.
- Alcohol in the mixture = 70% of 1000 ml = 0.70 * 1000 ml = 700 ml.

**Hint**: Calculate the quantities of water and alcohol based on the percentage given.

2. **Define the final condition**:
- We want the percentage of water in the new mixture to be 15%.
- Let \( x \) be the amount of alcohol to be added.

3. **Set up the equation**:
- After adding \( x \) ml of alcohol, the new total volume of the mixture will be \( 1000 + x \) ml.
- The amount of water remains the same at 300 ml.
- The new percentage of water can be expressed as:
\[ \frac{300}{1000 + x} = 0.15 \]

4. **Solve the equation**:
- Cross-multiply to eliminate the fraction:
\[ 300 = 0.15(1000 + x) \]
- Distributing the right side:
\[ 300 = 150 + 0.15x \]
- Rearranging the equation:
\[ 300 - 150 = 0.15x \]
\[ 150 = 0.15x \]
- Dividing both sides by 0.15:
\[ x = \frac{150}{0.15} = 1000 \text{ ml} \]

5. **Conclusion**:
- The amount of alcohol that must be added to the mixture is **1000 ml**.

### Final Answer:
The amount of alcohol that must be added is **1000 ml**.