To solve this problem, we need to determine the amount of alcohol in the initial mixture and then calculate the new percentage of alcohol after adding 3 liters of water.
Given that the initial mixture contains 20% alcohol and the rest is water, we can calculate the amount of alcohol in the 10 liters of mixture as follows:
Amount of alcohol = 20% of 10 liters = (20/100) * 10 liters = 2 liters
Since the rest of the mixture is water, the initial amount of water is:
Initial amount of water = Total mixture - Amount of alcohol = 10 liters - 2 liters = 8 liters
Now, when 3 liters of water are added to this mixture, the total amount of water becomes:
New amount of water = Initial amount of water + Added water = 8 liters + 3 liters = 11 liters
The total volume of the new mixture is the sum of the amount of alcohol and the amount of water:
Total volume of new mixture = Amount of alcohol + New amount of water = 2 liters + 11 liters = 13 liters
To calculate the new percentage of alcohol in the mixture, we divide the amount of alcohol by the total volume of the new mixture and multiply by 100:
New percentage of alcohol = (Amount of alcohol / Total volume of new mixture) * 100 = (2 liters / 13 liters) * 100 ≈ 15.38%
Therefore, the new mixture will contain approximately 15.38% alcohol after adding 3 liters of water.