Two jars ofcapacity 3 and 5 liters are filled with mixtures of alcohol...
Problem Solving: Percentage of Alcohol in the Cask
Given Information:
Two jars of capacity 3 and 5 liters are filled with mixtures of alcohol and water. In the smaller jar, 25% of the mixture is alcohol and in the larger, 25% of the mixture is water. The jars are emptied into a 9-liter cask, and the remaining volume is filled up with water.
Solution:
Step 1: Calculation of Amount of Alcohol in the Jars
To calculate the amount of alcohol in the jars, we need to know the volume of alcohol in each jar.
- In the smaller jar, 25% of the mixture is alcohol. Therefore, the volume of alcohol in the smaller jar is 0.25 x 3 liters = 0.75 liters.
- In the larger jar, 25% of the mixture is water. Therefore, the volume of alcohol in the larger jar is 0.75 x 5 liters = 1.25 liters.
Step 2: Calculation of Total Volume of Mixture
The total volume of the mixture in the cask is the sum of the volumes of the mixtures in the two jars.
- Total volume of mixture = 3 liters + 5 liters = 8 liters
Step 3: Calculation of Percentage of Alcohol in the Cask
The remaining volume in the cask is filled with water, so the total volume of the cask is 9 liters. Therefore, the volume of water in the cask is:
- Volume of water in the cask = 9 liters - 8 liters = 1 liter
To calculate the percentage of alcohol in the cask, we need to know the total volume of alcohol in the cask.
- Total volume of alcohol in the cask = 0.75 liters + 1.25 liters = 2 liters
Therefore, the percentage of alcohol in the cask is:
- Percentage of alcohol in the cask = (Total volume of alcohol / Total volume of mixture) x 100
- Percentage of alcohol in the cask = (2 liters / 9 liters) x 100 = 22.22%
Answer:
The percentage of alcohol in the cask is 22.22%.