A bottle of whisky contains` 42%` alcohol. Some part of this bottle is replaced by another bottle of whisky which contains `17%` alcohol. Now this mixture contains` 27%` alcohol. Which part of bottle has been replaced?

Answer

To solve the problem step-by-step, we will use the concept of alligation.

### Step-by-Step Solution:

1. **Identify the Concentrations**:
We have three concentrations:
- Concentration of the first whisky = 42% alcohol
- Concentration of the second whisky = 17% alcohol
- Concentration of the mixture = 27% alcohol

2. **Calculate the Differences**:
We will find the difference between the concentrations:
- Difference between the first whisky and the mixture:
\[ 42\% - 27\% = 15\% \]
- Difference between the second whisky and the mixture:
\[ 27\% - 17\% = 10\% \]

3. **Set Up the Alligation**:
According to the alligation rule, we can set up the ratio of the parts of the two whiskies:
- The ratio of the parts of the first whisky (42%) to the second whisky (17%) is given by the differences calculated:
\[ \text{Ratio} = \frac{10}{15} = \frac{2}{3} \]

4. **Assume Total Volume**:
Let's assume the total volume of the bottle is 5 units (this is an arbitrary choice to simplify calculations).

5. **Calculate the Parts**:
From the ratio \(2:3\):
- Parts of the first whisky = 2 units
- Parts of the second whisky = 3 units

6. **Determine the Replaced Part**:
Since we are replacing some part of the first whisky with the second whisky, the part replaced is equal to the parts of the second whisky:
- Replaced part = 3 units

7. **Calculate the Percentage of the Bottle Replaced**:
To find the percentage of the bottle that has been replaced:
\[ \text{Percentage replaced} = \left(\frac{\text{Replaced part}}{\text{Total volume}}\right) \times 100 = \left(\frac{3}{5}\right) \times 100 = 60\% \]

### Final Answer:
The part of the bottle that has been replaced is **60%**.