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A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y respectively. When 10 liter of the mixture is taken out and replaced it water, then the ratio becomes 2:3. Then what is the initial quantity of Milk in the Jar?
- a)12 Liter
- b)15 Liter
- c)18 Liter
- d)20 Liter
- e)None
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y...
x+y =30
(x-10*x/x+y)/ (y-10*y/(x+y) + 10) = 2/3
2x-4/3y = 20
x =18
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A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y...
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A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y...
Given:
- 30 liters mixture of Milk and Water in the ratio of x:y
- 10 liter of the mixture is taken out and replaced with water, then the ratio becomes 2:3
To find: Initial quantity of Milk in the Jar
Solution:
Let's assume the initial ratio of Milk and Water is x:y
So, we can write:
- Initial quantity of Milk = (x/ (x+y)) * 30
- Initial quantity of Water = (y/ (x+y)) * 30
Step 1: When 10 liters of mixture is taken out and replaced with water
- Let's assume that x liters of Milk and y liters of Water are in the jar initially
- So, the quantity of Milk in the jar = x/(x+y) * 30 liters
- Quantity of Milk taken out = (x/(x+y))*10 liters
- Quantity of Water taken out = (y/(x+y))*10 liters
After taking out 10 liters of mixture:
- Quantity of Milk in the jar = [(x/(x+y))*30] - [(x/(x+y))*10] = [(x/(x+y))*20] liters
- Quantity of Water in the jar = [(y/(x+y))*30] - [(y/(x+y))*10] = [(y/(x+y))*20] liters
Now, 10 liters of water is added to the jar:
- Quantity of Water in the jar = [(y/(x+y))*20] + 10 liters = [(y/(x+y))*20 + 10] liters
Step 2: The ratio of Milk and Water becomes 2:3
- According to the question, the ratio of Milk and Water after step 1 is 2:3
- So, we can write:
- Quantity of Milk in the jar = (2/5) * Total quantity of mixture
- Quantity of Water in the jar = (3/5) * Total quantity of mixture
- Quantity of Milk in the jar = 2/5 * [(x/(x+y))*20] liters
- Quantity of Water in the jar = 3/5 * [(y/(x+y))*20 + 10] liters
- Simplifying the above equations, we get:
- x/(x+y) = 2/5
- y/(x+y) = 3/5
Multiplying both equations, we get:
- (2/5) * (3/5) = (x/(x+y)) * (y/(x+y))
- 6/25 = xy/(x+y)^2
Let's assume k = x/y
So, we can write:
- y = 30/(k+1)
- x = 30k/(k+1)
Substituting the above values in the equation (xy/(x+y)^2 = 6/25), we get:
- (k/ (k+1)^2) = 6/25
- k = 3/2
So, the initial quantity of Milk in the jar = x/(x+y) * 30 = 18 liters
Therefore, the correct answer is option (c) 18 Liter.
- 30 liters mixture of Milk and Water in the ratio of x:y
- 10 liter of the mixture is taken out and replaced with water, then the ratio becomes 2:3
To find: Initial quantity of Milk in the Jar
Solution:
Let's assume the initial ratio of Milk and Water is x:y
So, we can write:
- Initial quantity of Milk = (x/ (x+y)) * 30
- Initial quantity of Water = (y/ (x+y)) * 30
Step 1: When 10 liters of mixture is taken out and replaced with water
- Let's assume that x liters of Milk and y liters of Water are in the jar initially
- So, the quantity of Milk in the jar = x/(x+y) * 30 liters
- Quantity of Milk taken out = (x/(x+y))*10 liters
- Quantity of Water taken out = (y/(x+y))*10 liters
After taking out 10 liters of mixture:
- Quantity of Milk in the jar = [(x/(x+y))*30] - [(x/(x+y))*10] = [(x/(x+y))*20] liters
- Quantity of Water in the jar = [(y/(x+y))*30] - [(y/(x+y))*10] = [(y/(x+y))*20] liters
Now, 10 liters of water is added to the jar:
- Quantity of Water in the jar = [(y/(x+y))*20] + 10 liters = [(y/(x+y))*20 + 10] liters
Step 2: The ratio of Milk and Water becomes 2:3
- According to the question, the ratio of Milk and Water after step 1 is 2:3
- So, we can write:
- Quantity of Milk in the jar = (2/5) * Total quantity of mixture
- Quantity of Water in the jar = (3/5) * Total quantity of mixture
- Quantity of Milk in the jar = 2/5 * [(x/(x+y))*20] liters
- Quantity of Water in the jar = 3/5 * [(y/(x+y))*20 + 10] liters
- Simplifying the above equations, we get:
- x/(x+y) = 2/5
- y/(x+y) = 3/5
Multiplying both equations, we get:
- (2/5) * (3/5) = (x/(x+y)) * (y/(x+y))
- 6/25 = xy/(x+y)^2
Let's assume k = x/y
So, we can write:
- y = 30/(k+1)
- x = 30k/(k+1)
Substituting the above values in the equation (xy/(x+y)^2 = 6/25), we get:
- (k/ (k+1)^2) = 6/25
- k = 3/2
So, the initial quantity of Milk in the jar = x/(x+y) * 30 = 18 liters
Therefore, the correct answer is option (c) 18 Liter.
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