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The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting mixture will have water and milk in the ratio.
- a)31:74
- b)31:75
- c)30:77
- d)30:74
- e)31:77
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed ...
We can establish the following ratios for two vessels:
Vessel 1: water to milk ratio is x to 2x.
Vessel 2: water to milk ratio is 2y to 5y.
We can set up the equation:
(x + 2x)/(2y + 5y) = 1/4
Simplifying, we get:
3x/7y = 1/4
Multiplying both sides by 12, we have:
12x = 7y
By choosing x = 7 and y = 12, we find:
Vessel 1: water = 7 and milk = 14
Vessel 2: water = 24 and milk = 60
Consequently, in the final mixture, the ratio of water to milk is:
(7 + 24)/(14 + 60) = 31/74
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Community Answer
The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed ...
Given:
- The vessels contain water and milk in the ratio 1:2
- The vessels contain water and milk in the ratio 2:5
- The mixture ratio is 1:4
To Find:
The ratio of water and milk in the resulting mixture.
Solution:
Let's assume the initial quantities of water and milk in the first vessel are 1x and 2x respectively.
Similarly, the initial quantities of water and milk in the second vessel are 2y and 5y respectively.
Mixing the Vessels:
When the two vessels are mixed in the ratio 1:4, the resulting mixture will have a total of 1+4=5 parts.
Calculating the Quantities of Water and Milk:
1. In the first vessel, the ratio of water to milk is 1:2. So, the total quantity of the mixture in the first vessel is 1x+2x=3x.
2. In the second vessel, the ratio of water to milk is 2:5. So, the total quantity of the mixture in the second vessel is 2y+5y=7y.
Calculating the Ratio of Water:
1. In the first vessel, the ratio of water to the total mixture is 1:3 (1x:3x).
2. In the second vessel, the ratio of water to the total mixture is 2:7 (2y:7y).
Calculating the Overall Ratio of Water:
For the resulting mixture, the ratio of water to the total mixture is 1:5 (1:4+1).
So, the ratio of water to the total mixture can be calculated by combining the ratios from both vessels:
(1x/3x + 2y/7y) / 2 = 1/5
Cross-multiplying:
7(1x) + 3(2y) = 2(3x)(5)
7x + 6y = 30x
6y = 23x
y/x = 23/6
Substituting the Value of y/x:
(1x/3x + 2(23/6)x/7(23/6)x) / 2 = 1/5
(1/3 + 46/84) / 2 = 1/5
(28/84 + 46/84) / 2 = 1/5
74/84 / 2 = 1/5
74/168 = 1/5
Simplifying the Ratio:
Dividing both numerator and denominator by 4:
(74/4)/(168/4) = 31/77
Conclusion:
Therefore, the resulting mixture will have water and milk in the ratio 31:77.
- The vessels contain water and milk in the ratio 1:2
- The vessels contain water and milk in the ratio 2:5
- The mixture ratio is 1:4
To Find:
The ratio of water and milk in the resulting mixture.
Solution:
Let's assume the initial quantities of water and milk in the first vessel are 1x and 2x respectively.
Similarly, the initial quantities of water and milk in the second vessel are 2y and 5y respectively.
Mixing the Vessels:
When the two vessels are mixed in the ratio 1:4, the resulting mixture will have a total of 1+4=5 parts.
Calculating the Quantities of Water and Milk:
1. In the first vessel, the ratio of water to milk is 1:2. So, the total quantity of the mixture in the first vessel is 1x+2x=3x.
2. In the second vessel, the ratio of water to milk is 2:5. So, the total quantity of the mixture in the second vessel is 2y+5y=7y.
Calculating the Ratio of Water:
1. In the first vessel, the ratio of water to the total mixture is 1:3 (1x:3x).
2. In the second vessel, the ratio of water to the total mixture is 2:7 (2y:7y).
Calculating the Overall Ratio of Water:
For the resulting mixture, the ratio of water to the total mixture is 1:5 (1:4+1).
So, the ratio of water to the total mixture can be calculated by combining the ratios from both vessels:
(1x/3x + 2y/7y) / 2 = 1/5
Cross-multiplying:
7(1x) + 3(2y) = 2(3x)(5)
7x + 6y = 30x
6y = 23x
y/x = 23/6
Substituting the Value of y/x:
(1x/3x + 2(23/6)x/7(23/6)x) / 2 = 1/5
(1/3 + 46/84) / 2 = 1/5
(28/84 + 46/84) / 2 = 1/5
74/84 / 2 = 1/5
74/168 = 1/5
Simplifying the Ratio:
Dividing both numerator and denominator by 4:
(74/4)/(168/4) = 31/77
Conclusion:
Therefore, the resulting mixture will have water and milk in the ratio 31:77.
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The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting mixture will have water and milk in the ratio.a)31:74b)31:75c)30:77d)30:74e)31:77Correct answer is option 'A'. Can you explain this answer?
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