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In a pot, the ratio of milk and water is 4 : 1. In another pot, the ratio of milk and water is 7 : 4. In what ratio mixture should be taken from both mixtures to make final mixture so that in final mixture the ratio of milk and water be 41 : 14?
- a)3 : 2
- b)2 : 1
- c)4 : 3
- d)5 : 2
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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In a pot, the ratio of milk and water is 4 : 1. In another pot, the ra...
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In a pot, the ratio of milk and water is 4 : 1. In another pot, the ra...
To solve this question, we need to find the ratio in which the mixtures should be taken from both pots to obtain the desired ratio of milk and water in the final mixture.
Let's assume that we take x units of the first mixture from the pot with a ratio of 4:1, and y units of the second mixture from the pot with a ratio of 7:4.
Step 1: Calculate the amount of milk and water in the first mixture
In the first pot, the ratio of milk to water is 4:1. This means that out of every 4+1=5 units of the mixture, 4 units are milk and 1 unit is water.
So, the amount of milk in the first mixture = (4/5) * x
And the amount of water in the first mixture = (1/5) * x
Step 2: Calculate the amount of milk and water in the second mixture
In the second pot, the ratio of milk to water is 7:4. This means that out of every 7+4=11 units of the mixture, 7 units are milk and 4 units are water.
So, the amount of milk in the second mixture = (7/11) * y
And the amount of water in the second mixture = (4/11) * y
Step 3: Calculate the total amount of milk and water in the final mixture
According to the given ratio of milk to water in the final mixture (41:14), the total ratio is 41+14=55.
So, the amount of milk in the final mixture = (41/55) * (x+y)
And the amount of water in the final mixture = (14/55) * (x+y)
Step 4: Set up the equation
Since the amount of milk and water in the final mixture should be equal to the sum of the amounts from the first and second mixtures, we can set up the following equation:
(4/5) * x + (7/11) * y = (41/55) * (x+y) [equating the amount of milk]
(1/5) * x + (4/11) * y = (14/55) * (x+y) [equating the amount of water]
Step 5: Solve the equations
To solve these equations, we can multiply both sides of each equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
Multiplying both sides of the first equation by 55*5 and the second equation by 55*11, we get:
44x + 35y = 41x + 41y [equation 1]
11x + 20y = 14x + 14y [equation 2]
Simplifying these equations, we get:
3x = 6y [equation 3]
3x = 6y [equation 4]
Since equation 3 and equation 4 are the same, it means that x = y.
Step 6: Determine the ratio
Since x = y, the ratio of the mixtures taken from both pots is 1:1.
Therefore, the correct answer is option B) 2:1.
Let's assume that we take x units of the first mixture from the pot with a ratio of 4:1, and y units of the second mixture from the pot with a ratio of 7:4.
Step 1: Calculate the amount of milk and water in the first mixture
In the first pot, the ratio of milk to water is 4:1. This means that out of every 4+1=5 units of the mixture, 4 units are milk and 1 unit is water.
So, the amount of milk in the first mixture = (4/5) * x
And the amount of water in the first mixture = (1/5) * x
Step 2: Calculate the amount of milk and water in the second mixture
In the second pot, the ratio of milk to water is 7:4. This means that out of every 7+4=11 units of the mixture, 7 units are milk and 4 units are water.
So, the amount of milk in the second mixture = (7/11) * y
And the amount of water in the second mixture = (4/11) * y
Step 3: Calculate the total amount of milk and water in the final mixture
According to the given ratio of milk to water in the final mixture (41:14), the total ratio is 41+14=55.
So, the amount of milk in the final mixture = (41/55) * (x+y)
And the amount of water in the final mixture = (14/55) * (x+y)
Step 4: Set up the equation
Since the amount of milk and water in the final mixture should be equal to the sum of the amounts from the first and second mixtures, we can set up the following equation:
(4/5) * x + (7/11) * y = (41/55) * (x+y) [equating the amount of milk]
(1/5) * x + (4/11) * y = (14/55) * (x+y) [equating the amount of water]
Step 5: Solve the equations
To solve these equations, we can multiply both sides of each equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
Multiplying both sides of the first equation by 55*5 and the second equation by 55*11, we get:
44x + 35y = 41x + 41y [equation 1]
11x + 20y = 14x + 14y [equation 2]
Simplifying these equations, we get:
3x = 6y [equation 3]
3x = 6y [equation 4]
Since equation 3 and equation 4 are the same, it means that x = y.
Step 6: Determine the ratio
Since x = y, the ratio of the mixtures taken from both pots is 1:1.
Therefore, the correct answer is option B) 2:1.
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In a pot, the ratio of milk and water is 4 : 1. In another pot, the ratio of milk and water is 7 : 4. In what ratio mixture should be taken from both mixtures to make final mixture so that in final mixture the ratio of milk and water be 41 : 14?a)3 : 2b)2 : 1c)4 : 3d)5 : 2e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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