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Two pots A and B contain syrup and water in the ratio 3:7 and 5:2 respectively. Find the ratio in which these mixtures be mixed to get a new mixture containing syrup and water in the ratio of 2:3?
- a)22:7
- b)4:3
- c)16:9
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two pots A and B contain syrup and water in the ratio 3:7 and 5:2 resp...
The syrup in pot A is 3/10 and in pot B is 5/7. In the required mixture the syrup should be 2/5. Using Alligation we have
⇒ The required ratio is 22: 7.
Most Upvoted Answer
Two pots A and B contain syrup and water in the ratio 3:7 and 5:2 resp...
Given:
Pot A contains syrup and water in the ratio 3:7
Pot B contains syrup and water in the ratio 5:2
To find:
The ratio in which the mixtures from pots A and B should be mixed to obtain a new mixture containing syrup and water in the ratio of 2:3
Solution:
Let's assume that we mix x units from pot A and y units from pot B to obtain the new mixture.
Ratio of syrup in pot A:
The ratio of syrup in pot A is 3:7. This means that for every 3 parts of syrup, there are 7 parts of water.
Ratio of syrup in pot B:
The ratio of syrup in pot B is 5:2. This means that for every 5 parts of syrup, there are 2 parts of water.
Ratio of syrup in the new mixture:
Since the new mixture should have a ratio of syrup to water of 2:3, this means that for every 2 parts of syrup, there should be 3 parts of water.
Equations:
Based on the given information, we can set up the following equations:
For syrup:
(3x/10) + (5y/7) = (2(x+y)/5)
For water:
(7x/10) + (2y/7) = (3(x+y)/5)
Solving the equations:
Multiplying the first equation by 10 and the second equation by 5 to eliminate the denominators, we get:
3x + (50y/7) = 4x + (4y/7)
7x + (20y/7) = 6x + (6y/7)
Simplifying the equations, we have:
(50y/7) - (4y/7) = 4x - 3x
(20y/7) - (6y/7) = 6x - 7x
(46y/7) = x
(14y/7) = x
x = 2y
Therefore, the ratio of the mixtures from pots A and B should be 2y:y, which simplifies to 2:1.
Hence, the correct ratio is 2:1, which is equivalent to 22:7 (multiplying by 7).
Therefore, the correct answer is option A) 22:7.
Pot A contains syrup and water in the ratio 3:7
Pot B contains syrup and water in the ratio 5:2
To find:
The ratio in which the mixtures from pots A and B should be mixed to obtain a new mixture containing syrup and water in the ratio of 2:3
Solution:
Let's assume that we mix x units from pot A and y units from pot B to obtain the new mixture.
Ratio of syrup in pot A:
The ratio of syrup in pot A is 3:7. This means that for every 3 parts of syrup, there are 7 parts of water.
Ratio of syrup in pot B:
The ratio of syrup in pot B is 5:2. This means that for every 5 parts of syrup, there are 2 parts of water.
Ratio of syrup in the new mixture:
Since the new mixture should have a ratio of syrup to water of 2:3, this means that for every 2 parts of syrup, there should be 3 parts of water.
Equations:
Based on the given information, we can set up the following equations:
For syrup:
(3x/10) + (5y/7) = (2(x+y)/5)
For water:
(7x/10) + (2y/7) = (3(x+y)/5)
Solving the equations:
Multiplying the first equation by 10 and the second equation by 5 to eliminate the denominators, we get:
3x + (50y/7) = 4x + (4y/7)
7x + (20y/7) = 6x + (6y/7)
Simplifying the equations, we have:
(50y/7) - (4y/7) = 4x - 3x
(20y/7) - (6y/7) = 6x - 7x
(46y/7) = x
(14y/7) = x
x = 2y
Therefore, the ratio of the mixtures from pots A and B should be 2y:y, which simplifies to 2:1.
Hence, the correct ratio is 2:1, which is equivalent to 22:7 (multiplying by 7).
Therefore, the correct answer is option A) 22:7.
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