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Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?
- a)6:1
- b)5:4
- c)20:7
- d)10:9
- e)14:11
Correct answer is option 'C'. Can you explain this answer?
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Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what...
Approach:
To find the proportion in which two mixtures should be mixed, we can set up a system of equations based on the given ratios of X and Y in the mixtures.
Given ratios:
1. Mixture 1: X:Y = 3:2
2. Mixture 2: X:Y = 3:4
3. Final Mixture: X:Y = 5:4
Let the quantities of the two mixtures be m and n:
- Quantity of X in Mixture 1 = 3m/5
- Quantity of Y in Mixture 1 = 2m/5
- Quantity of X in Mixture 2 = 3n/7
- Quantity of Y in Mixture 2 = 4n/7
- Quantity of X in Final Mixture = 5/9(m + n)
- Quantity of Y in Final Mixture = 4/9(m + n)
Equating the quantities:
- 3m/5 + 3n/7 = 5/9(m + n) (From X component)
- 2m/5 + 4n/7 = 4/9(m + n) (From Y component)
Solving the above equations:
- Simplify the equations and solve for m/n
- After solving, we get m:n = 20:7
Therefore, the two mixtures should be mixed in the proportion of 20:7 to get a new mixture in which the ratio of X to Y is 5:4.
To find the proportion in which two mixtures should be mixed, we can set up a system of equations based on the given ratios of X and Y in the mixtures.
Given ratios:
1. Mixture 1: X:Y = 3:2
2. Mixture 2: X:Y = 3:4
3. Final Mixture: X:Y = 5:4
Let the quantities of the two mixtures be m and n:
- Quantity of X in Mixture 1 = 3m/5
- Quantity of Y in Mixture 1 = 2m/5
- Quantity of X in Mixture 2 = 3n/7
- Quantity of Y in Mixture 2 = 4n/7
- Quantity of X in Final Mixture = 5/9(m + n)
- Quantity of Y in Final Mixture = 4/9(m + n)
Equating the quantities:
- 3m/5 + 3n/7 = 5/9(m + n) (From X component)
- 2m/5 + 4n/7 = 4/9(m + n) (From Y component)
Solving the above equations:
- Simplify the equations and solve for m/n
- After solving, we get m:n = 20:7
Therefore, the two mixtures should be mixed in the proportion of 20:7 to get a new mixture in which the ratio of X to Y is 5:4.
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Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?a)6:1b)5:4c)20:7d)10:9e)14:11Correct answer is option 'C'. Can you explain this answer?
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