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A mixture contains wine and water in the ratio of 5 : 2 respectively and another mixture contains them in the ratio of 4 : 5 respectively. How many liters of the latter must be mixed with 35 liters of the former so that the resultant mixture must contain equal quantities of wine and water?
  • a)
    90 liters
  • b)
    100 liters
  • c)
    105 liters
  • d)
    135 liters
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A mixture contains wine and water in the ratio of 5 : 2 respectively a...

Water in former = 35 – 25 = 10 liters
Let wine in latter = 4x
Water in latter = 5x
25 + 4x = 10 + 5x
5x – 4x = 25 – 10
x = 15 liters
So the answer = 4x + 5x = 9 × 15 = 135 liters
Hence, option C is correct.
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Community Answer
A mixture contains wine and water in the ratio of 5 : 2 respectively a...
Understanding the Mixtures
To solve the problem, we need to analyze the two mixtures and their compositions of wine and water.
Mixture 1: 35 liters
- Ratio of wine to water: 5:2
- Total parts = 5 + 2 = 7 parts
- Wine in Mixture 1 = (5/7) * 35 = 25 liters
- Water in Mixture 1 = (2/7) * 35 = 10 liters
Mixture 2: Unknown Quantity (x liters)
- Ratio of wine to water: 4:5
- Total parts = 4 + 5 = 9 parts
- Wine in Mixture 2 = (4/9) * x liters
- Water in Mixture 2 = (5/9) * x liters
Setting Up the Equation
We need to mix the two mixtures so that the quantities of wine and water are equal in the resultant mixture.
- Total Wine = Wine from Mixture 1 + Wine from Mixture 2
- Total Water = Water from Mixture 1 + Water from Mixture 2
Setting them equal gives us:
25 + (4/9)x = 10 + (5/9)x
Solving the Equation
1. Rearranging gives:
- 25 - 10 = (5/9)x - (4/9)x
- 15 = (1/9)x
2. Multiplying both sides by 9 results in:
- x = 15 * 9 = 135 liters
Conclusion
To achieve equal quantities of wine and water, we need to mix 135 liters of the second mixture with 35 liters of the first mixture.
Therefore, the correct answer is option D: 135 liters.
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A mixture contains wine and water in the ratio of 5 : 2 respectively and another mixture contains them in the ratio of 4 : 5 respectively. How many liters of the latter must be mixed with 35 liters of the former so that the resultant mixture must contain equal quantities of wine and water?a)90 litersb)100 litersc)105 litersd)135 litersCorrect answer is option 'D'. Can you explain this answer?
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