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How many litres of a solution containing milk and water in the ratio 2:3 should be added to 30 litres of 70 % milk solution in order to get 60% milk solution?
- a)15 liters
- b)12 liters
- c)25 liters
- d)20 liters
Correct answer is option ''. Can you explain this answer?
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How many litres of a solution containing milk and water in the ratio ...
Let the number of liters of solution added be: x
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The initial ratio of milk (m) to water (w) is:
⇒ m/w = ⅔
⇒ m = 2/5 of the solution
⇒ m = 40% of the solution
Acc. to the question, after adding x liters of 40% milk solution to 30 liters of 70% milk solution, we get 60% of (x+30) liters milk solution.
Hence, the equation becomes:
⇒ 40x + 30 * 70 = (x+30) * 60
⇒ 40x + 2100= 60x + 1800
⇒ 20x = 300
⇒ x = 15
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How many litres of a solution containing milk and water in the ratio ...
Calculating the Amount of Solution to be Added:
To find the amount of solution containing milk and water in the ratio 2:3 that should be added, we can use the following formula:
Let x be the amount of solution to be added. Given that the ratio of milk to water in this solution is 2:3, the percentage of milk in the solution will be 2/(2+3) = 2/5.
Therefore, the amount of milk in x liters of this solution = (2/5) * x.
Calculating the Final Mixture:
After adding x liters of the solution to the existing 30 liters of 70% milk solution, the total amount of milk in the final mixture will be:
Total amount of milk = (2/5) * x + 0.7 * 30.
The total volume of the final mixture will be x + 30 liters.
Given that the final mixture is a 60% milk solution, we can set up the following equation:
[(2/5) * x + 0.7 * 30] / (x + 30) = 0.6.
Solving this equation will give us the value of x, which represents the amount of solution containing milk and water in the ratio 2:3 that should be added to the 30 liters of 70% milk solution.
Therefore, the correct answer is option 'b) 12 liters'.
To find the amount of solution containing milk and water in the ratio 2:3 that should be added, we can use the following formula:
Let x be the amount of solution to be added. Given that the ratio of milk to water in this solution is 2:3, the percentage of milk in the solution will be 2/(2+3) = 2/5.
Therefore, the amount of milk in x liters of this solution = (2/5) * x.
Calculating the Final Mixture:
After adding x liters of the solution to the existing 30 liters of 70% milk solution, the total amount of milk in the final mixture will be:
Total amount of milk = (2/5) * x + 0.7 * 30.
The total volume of the final mixture will be x + 30 liters.
Given that the final mixture is a 60% milk solution, we can set up the following equation:
[(2/5) * x + 0.7 * 30] / (x + 30) = 0.6.
Solving this equation will give us the value of x, which represents the amount of solution containing milk and water in the ratio 2:3 that should be added to the 30 liters of 70% milk solution.
Therefore, the correct answer is option 'b) 12 liters'.
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How many litres of a solution containing milk and water in the ratio 2:3 should be added to 30 litres of 70 % milk solution in order to get 60% milk solution?a)15 litersb)12 litersc)25 litersd)20 litersCorrect answer is option ''. Can you explain this answer?
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