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How many litres of water must be added to 60 litre mixture that contains milk and water in the 7:3 such that the resulting mixture has 50% water in it?
- a)12
- b)16
- c)24
- d)28
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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How many litres of water must be added to 60 litre mixture that contai...
Answer – c) 24 Explanation : milk = (7/10)*60 = 42 and water = 18 so water must be added = 42 – 18 = 24
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How many litres of water must be added to 60 litre mixture that contai...
Problem: To find the amount of water that must be added to a 60-litre mixture of milk and water in the ratio 7:3 to make it 50% water.
Solution:
Step 1: Let's assume that the mixture contains 7x litres of milk and 3x litres of water.
Step 2: Now, we need to find out the total amount of water in the original mixture.
Total amount of water = 3x litres
Step 3: We want to make the resulting mixture 50% water.
Therefore, the total amount of water in the resulting mixture should be half of the total volume of the resulting mixture.
Let's assume that we need to add y litres of water to the original mixture to make it 50% water.
So, the total volume of the resulting mixture = 60 + y litres
The total amount of water in the resulting mixture = (50/100) * (60 + y) = 30 + (y/2) litres
Step 4: Now, we can form an equation based on the information we have.
Total amount of water in the original mixture + Amount of water added = Total amount of water in the resulting mixture
3x + y = 30 + (y/2)
6x + 2y = 60 + y
6x - y = 60
Step 5: We know that the original mixture has 7x litres of milk and 3x litres of water.
We need to add y litres of water to the original mixture.
Therefore, the resulting mixture will have 7x litres of milk and (3x + y) litres of water.
We want the resulting mixture to have 50% water.
(3x + y) = (50/100) * (60 + y)
3x + y = 30 + (y/2)
6x + 2y = 60 + y
6x - y = 60
Solving the above two equations, we get
x = 5, y = 24
So, we need to add 24 litres of water to the original mixture to make it 50% water.
Therefore, the correct option is (C) 24.
Solution:
Step 1: Let's assume that the mixture contains 7x litres of milk and 3x litres of water.
Step 2: Now, we need to find out the total amount of water in the original mixture.
Total amount of water = 3x litres
Step 3: We want to make the resulting mixture 50% water.
Therefore, the total amount of water in the resulting mixture should be half of the total volume of the resulting mixture.
Let's assume that we need to add y litres of water to the original mixture to make it 50% water.
So, the total volume of the resulting mixture = 60 + y litres
The total amount of water in the resulting mixture = (50/100) * (60 + y) = 30 + (y/2) litres
Step 4: Now, we can form an equation based on the information we have.
Total amount of water in the original mixture + Amount of water added = Total amount of water in the resulting mixture
3x + y = 30 + (y/2)
6x + 2y = 60 + y
6x - y = 60
Step 5: We know that the original mixture has 7x litres of milk and 3x litres of water.
We need to add y litres of water to the original mixture.
Therefore, the resulting mixture will have 7x litres of milk and (3x + y) litres of water.
We want the resulting mixture to have 50% water.
(3x + y) = (50/100) * (60 + y)
3x + y = 30 + (y/2)
6x + 2y = 60 + y
6x - y = 60
Solving the above two equations, we get
x = 5, y = 24
So, we need to add 24 litres of water to the original mixture to make it 50% water.
Therefore, the correct option is (C) 24.
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How many litres of water must be added to 60 litre mixture that contains milk and water in the 7:3 such that the resulting mixture has 50% water in it?a)12b)16c)24d)28e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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