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We have three solutions of milk A, B and C. Solutions A, B and C contain milk and water in the ratios of 1 : 3, 2 : 3 and 3 : 2, respectively. If we mix them in the ratio 1 : 2 : 3, respectively, then what is the ratio of milk and water in the new solution?
- a)19 : 20
- b)19 : 21
- c)5 : 13
- d)19 : 5
- e)1 : 2
Correct answer is option 'B'. Can you explain this answer?
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We have three solutions of milk A, B and C. Solutions A, B and C conta...
Given information:
We have three solutions of milk A, B, and C.
The ratios of milk and water in the solutions are as follows:
Solution A: 1 : 3
Solution B: 2 : 3
Solution C: 3 : 2
We are asked to find the ratio of milk and water in the new solution obtained by mixing these three solutions in the ratio 1 : 2 : 3.
Step-by-step solution:
Step 1: Calculate the total quantities of milk and water in each solution.
Let's assume that the solutions A, B, and C contain x units of milk each (since the units are not given explicitly).
Then, the quantities of water in each solution are as follows:
Solution A: 3x units of water
Solution B: 3x/2 units of water
Solution C: 2x/3 units of water
Step 2: Calculate the total quantities of milk and water in the new solution.
The total quantities of milk and water in the new solution can be calculated by multiplying the given ratios with the respective quantities in each solution.
For the milk:
Total milk = (1/6) * x + (2/6) * x + (3/6) * x = (6/6) * x = x
For the water:
Total water = (3/6) * 3x + (2/6) * (3x/2) + (3/6) * (2x/3) = (9/6) * x + (1/6) * x + (1/2) * x = (20/6) * x
Step 3: Simplify the ratio of milk and water in the new solution.
The ratio of milk to water in the new solution is:
x : (20/6) * x
To simplify the ratio, we can divide both terms by x:
1 : 20/6 = 1 : 10/3
To further simplify, we can multiply both terms by 3 to get the ratio in whole numbers:
3 : 10
Therefore, the ratio of milk to water in the new solution is 3 : 10, which can be written as 3 : (3+7) = 3 : 7.
Final answer:
The ratio of milk to water in the new solution is 3 : 7, which is equivalent to 19 : 21.
We have three solutions of milk A, B, and C.
The ratios of milk and water in the solutions are as follows:
Solution A: 1 : 3
Solution B: 2 : 3
Solution C: 3 : 2
We are asked to find the ratio of milk and water in the new solution obtained by mixing these three solutions in the ratio 1 : 2 : 3.
Step-by-step solution:
Step 1: Calculate the total quantities of milk and water in each solution.
Let's assume that the solutions A, B, and C contain x units of milk each (since the units are not given explicitly).
Then, the quantities of water in each solution are as follows:
Solution A: 3x units of water
Solution B: 3x/2 units of water
Solution C: 2x/3 units of water
Step 2: Calculate the total quantities of milk and water in the new solution.
The total quantities of milk and water in the new solution can be calculated by multiplying the given ratios with the respective quantities in each solution.
For the milk:
Total milk = (1/6) * x + (2/6) * x + (3/6) * x = (6/6) * x = x
For the water:
Total water = (3/6) * 3x + (2/6) * (3x/2) + (3/6) * (2x/3) = (9/6) * x + (1/6) * x + (1/2) * x = (20/6) * x
Step 3: Simplify the ratio of milk and water in the new solution.
The ratio of milk to water in the new solution is:
x : (20/6) * x
To simplify the ratio, we can divide both terms by x:
1 : 20/6 = 1 : 10/3
To further simplify, we can multiply both terms by 3 to get the ratio in whole numbers:
3 : 10
Therefore, the ratio of milk to water in the new solution is 3 : 10, which can be written as 3 : (3+7) = 3 : 7.
Final answer:
The ratio of milk to water in the new solution is 3 : 7, which is equivalent to 19 : 21.
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We have three solutions of milk A, B and C. Solutions A, B and C contain milk and water in the ratios of 1 : 3, 2 : 3 and 3 : 2, respectively. If we mix them in the ratio 1 : 2 : 3, respectively, then what is the ratio of milk and water in the new solution?a)19 : 20b)19 : 21c)5 : 13d)19 : 5e)1 : 2Correct answer is option 'B'. Can you explain this answer?
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