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The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
- a)65%
- b)70%
- c)75%
- d)80%
- e)None of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The ratio of alcohol and water in three mixtures of alcohol and water ...
Given:
The ratio of alcohol and water in three mixtures is 3:2, 4:1, and 7:3.
To find:
The concentration of alcohol in the resulting mixture.
Solution:
Let's assume that the quantities of the mixture drawn and mixed are x each.
Mixture 1:
Ratio of alcohol to water is 3:2.
So, the quantity of alcohol in mixture 1 = (3/5)x
And the quantity of water in mixture 1 = (2/5)x
Mixture 2:
Ratio of alcohol to water is 4:1.
So, the quantity of alcohol in mixture 2 = (4/5)x
And the quantity of water in mixture 2 = (1/5)x
Mixture 3:
Ratio of alcohol to water is 7:3.
So, the quantity of alcohol in mixture 3 = (7/10)x
And the quantity of water in mixture 3 = (3/10)x
Final mixture:
In the final mixture, the quantities of alcohol and water from each individual mixture will be added together.
The quantity of alcohol in the final mixture = (3/5)x + (4/5)x + (7/10)x
= (6/10)x + (8/10)x + (7/10)x
= (21/10)x
The quantity of water in the final mixture = (2/5)x + (1/5)x + (3/10)x
= (4/10)x + (2/10)x + (3/10)x
= (9/10)x
Concentration of alcohol in the final mixture:
To find the concentration of alcohol, we need to calculate the ratio of alcohol to the total mixture.
Concentration of alcohol in the final mixture = (quantity of alcohol in the final mixture) / (quantity of alcohol + quantity of water in the final mixture)
= (21/10)x / [(21/10)x + (9/10)x]
= (21/10)x / (30/10)x
= (21/10)/(30/10)
= (21/10) * (10/30)
= 21/30
= 7/10
= 0.7
Therefore, the concentration of alcohol in the resulting mixture is 70%, which is option (b).
The ratio of alcohol and water in three mixtures is 3:2, 4:1, and 7:3.
To find:
The concentration of alcohol in the resulting mixture.
Solution:
Let's assume that the quantities of the mixture drawn and mixed are x each.
Mixture 1:
Ratio of alcohol to water is 3:2.
So, the quantity of alcohol in mixture 1 = (3/5)x
And the quantity of water in mixture 1 = (2/5)x
Mixture 2:
Ratio of alcohol to water is 4:1.
So, the quantity of alcohol in mixture 2 = (4/5)x
And the quantity of water in mixture 2 = (1/5)x
Mixture 3:
Ratio of alcohol to water is 7:3.
So, the quantity of alcohol in mixture 3 = (7/10)x
And the quantity of water in mixture 3 = (3/10)x
Final mixture:
In the final mixture, the quantities of alcohol and water from each individual mixture will be added together.
The quantity of alcohol in the final mixture = (3/5)x + (4/5)x + (7/10)x
= (6/10)x + (8/10)x + (7/10)x
= (21/10)x
The quantity of water in the final mixture = (2/5)x + (1/5)x + (3/10)x
= (4/10)x + (2/10)x + (3/10)x
= (9/10)x
Concentration of alcohol in the final mixture:
To find the concentration of alcohol, we need to calculate the ratio of alcohol to the total mixture.
Concentration of alcohol in the final mixture = (quantity of alcohol in the final mixture) / (quantity of alcohol + quantity of water in the final mixture)
= (21/10)x / [(21/10)x + (9/10)x]
= (21/10)x / (30/10)x
= (21/10)/(30/10)
= (21/10) * (10/30)
= 21/30
= 7/10
= 0.7
Therefore, the concentration of alcohol in the resulting mixture is 70%, which is option (b).
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Community Answer
The ratio of alcohol and water in three mixtures of alcohol and water ...
To find the concentration of alcohol in the resulting mixture, we need to consider the ratios and quantities of alcohol and water in each of the initial mixtures.
Let's assume we have equal quantities of the three mixtures: Mixture 1, Mixture 2, and Mixture 3.
The ratio of alcohol to water in Mixture 1 is 3:2, meaning for every 3 parts of alcohol, there are 2 parts of water.
The ratio of alcohol to water in Mixture 2 is 4:1, meaning for every 4 parts of alcohol, there is 1 part of water.
The ratio of alcohol to water in Mixture 3 is 7:3, meaning for every 7 parts of alcohol, there are 3 parts of water.
To find the resulting concentration of alcohol in the mixture, we need to calculate the total amount of alcohol and water.
Total alcohol = (3 + 4 + 7) parts
Total water = (2 + 1 + 3) parts
Total water = (2 + 1 + 3) parts
The resulting concentration of alcohol in the mixture can be calculated as:
Concentration of alcohol = (Total alcohol) / (Total alcohol + Total water)
Concentration of alcohol = (Total alcohol) / (Total alcohol + Total water)
Concentration of alcohol = (3 + 4 + 7) / ((3 + 4 + 7) + (2 + 1 + 3))
Concentration of alcohol = 14 / 20
Concentration of alcohol = 0.7 or 70%
Therefore, the resulting concentration of alcohol in the mixture is 70%.
The correct answer is B: 70%.
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