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In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?
- a)80 litres
- b)70 litres
- c)75 litres
- d)96 litres
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a mixture of wine and water, there is only 28% water. After replaci...
GIVEN:
Water = 28%
After Replacing, the mixture with 5 litres of pure wine
Wine = 74%
CALCULATION:
Ratio = 13 : 1
Initial mixture = 13 + 1 = 14 units
Mixture = 14 × 5 = 70 litre
Most Upvoted Answer
In a mixture of wine and water, there is only 28% water. After replaci...
To solve this problem, we'll use the concept of percentages and algebraic equations.
Let's assume the quantity of the mixture is 'x' liters.
Step 1: Initial Mixture
In the initial mixture, the percentage of water is 28%, which means the percentage of wine is 100% - 28% = 72%.
So, the quantity of wine in the initial mixture = 72% of x liters = 0.72x
And the quantity of water in the initial mixture = 28% of x liters = 0.28x
Step 2: Replacing the Mixture
After replacing the mixture with 5 liters of pure wine, the quantity of wine becomes (0.72x + 5) liters.
Step 3: Final Mixture
In the final mixture, the percentage of wine is given as 74%, which means the percentage of water is 100% - 74% = 26%.
So, the quantity of wine in the final mixture = 74% of (x + 5) liters = 0.74(x + 5)
And the quantity of water in the final mixture = 26% of (x + 5) liters = 0.26(x + 5)
Step 4: Setting up the Equation
Since the quantity of wine in the initial mixture is the same as the quantity of wine in the final mixture, we can set up the equation:
0.72x + 5 = 0.74(x + 5)
Step 5: Solving the Equation
Let's solve the equation to find the value of 'x':
0.72x + 5 = 0.74x + 3.7
0.74x - 0.72x = 5 - 3.7
0.02x = 1.3
x = 1.3 / 0.02
x = 65
Therefore, the quantity of the mixture is 65 liters.
Let's assume the quantity of the mixture is 'x' liters.
Step 1: Initial Mixture
In the initial mixture, the percentage of water is 28%, which means the percentage of wine is 100% - 28% = 72%.
So, the quantity of wine in the initial mixture = 72% of x liters = 0.72x
And the quantity of water in the initial mixture = 28% of x liters = 0.28x
Step 2: Replacing the Mixture
After replacing the mixture with 5 liters of pure wine, the quantity of wine becomes (0.72x + 5) liters.
Step 3: Final Mixture
In the final mixture, the percentage of wine is given as 74%, which means the percentage of water is 100% - 74% = 26%.
So, the quantity of wine in the final mixture = 74% of (x + 5) liters = 0.74(x + 5)
And the quantity of water in the final mixture = 26% of (x + 5) liters = 0.26(x + 5)
Step 4: Setting up the Equation
Since the quantity of wine in the initial mixture is the same as the quantity of wine in the final mixture, we can set up the equation:
0.72x + 5 = 0.74(x + 5)
Step 5: Solving the Equation
Let's solve the equation to find the value of 'x':
0.72x + 5 = 0.74x + 3.7
0.74x - 0.72x = 5 - 3.7
0.02x = 1.3
x = 1.3 / 0.02
x = 65
Therefore, the quantity of the mixture is 65 liters.
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In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer?
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In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer?.
In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer?.
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In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of In a mixture of wine and water, there is only 28% water. After replacing the mixture with 5 litres of pure wine, the percentage of wine in the mixture becomes 74%. Find the quantity of mixture?a)80 litresb)70 litresc)75 litresd)96 litresCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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