A large tub is filled with 920 liters of water and 1,800 liters of alcohol. If `40%` of the alcohol evaporates, what percemt of the remaining liquid is water?

Answer

To solve the problem step by step, let's follow the given information and calculations:

1. **Identify the initial volumes of water and alcohol:**
- Water = 920 liters
- Alcohol = 1800 liters

2. **Calculate the amount of alcohol that evaporates:**
- It is given that 40% of the alcohol evaporates.
- To find the volume of alcohol that evaporates, we calculate:
\[ \text{Evaporated Alcohol} = 40\% \text{ of } 1800 \text{ liters} = \frac{40}{100} \times 1800 = 720 \text{ liters} \]

3. **Determine the remaining volume of alcohol:**
- After evaporation, the remaining volume of alcohol is:
\[ \text{Remaining Alcohol} = 1800 \text{ liters} - 720 \text{ liters} = 1080 \text{ liters} \]

4. **Calculate the total volume of the remaining liquid:**
- The total volume of the remaining liquid (water + remaining alcohol) is:
\[ \text{Total Remaining Liquid} = \text{Water} + \text{Remaining Alcohol} = 920 \text{ liters} + 1080 \text{ liters} = 2000 \text{ liters} \]

5. **Find the percentage of the remaining liquid that is water:**
- The percentage of water in the remaining liquid is calculated as:
\[ \text{Percentage of Water} = \left( \frac{\text{Volume of Water}}{\text{Total Remaining Liquid}} \right) \times 100 = \left( \frac{920}{2000} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Percentage of Water} = \left( 0.46 \right) \times 100 = 46\% \]

Thus, the percentage of the remaining liquid that is water is **46%**.