Correct option is C
Solution:
Problem Restatement:
We have two vessels:
1.
First vessel contains
3/8 L of alcohol and water is added to make the total volume
1 L.
2.
Second vessel contains
2/7 L of alcohol and water is added to make the total volume
1 L. The question asks us to find the
alcohol to water ratio when both solutions are mixed.
Step 1: Alcohol and water in each vessel
First vessel:
· Alcohol = 3/8 L.
· Water added = 1 - 3/8 = 5/8 L.
So, the first vessel contains:
· Alcohol = 3/8 L
· Water = 5/8 L
Second vessel:
· Alcohol = 2/7 L.
· Water added = 1 - 2/7 = 5/7 L.
So, the second vessel contains:
· Alcohol = 2/7 L
· Water = 5/7 L
Step 2: Total alcohol and total water in the mixed solution
When the two solutions are mixed, the total alcohol and total water are the sum of the alcohol and water from both vessels.
Total alcohol:
Total alcohol = 3/8 + 2/7
To add these, we need to find the least common denominator (LCD), which is 56:
· 3/8 = 21/56
· 2/7 = 16/56
Total alcohol = 21/56 + 16/56 = 37/56 L.
Total water:
Total water = 5/8 + 5/7
Again, we find the LCD, which is 56:
· 5/8 = 35/56
· 5/7 = 40/56
Total water = 35/56 + 40/56 = 75/56 L.
Step 3: Alcohol-to-water ratio
Now, we find the ratio of alcohol to water: Alcohol to water ratio = (37/56) / (75/56)
Simplifying: Alcohol to water ratio = 37/75.
This simplifies to approximately 1:2.
Conclusion:
The alcohol-to-water ratio in the mixed solution is approximately
1:2.
