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30 litre of solution contains alcohol and water in the ratio 2:3. How much alcohol must be added to the solution to make a solution containing 60% of alcohol?
  • a)
    10
  • b)
    12
  • c)
    14
  • d)
    15
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
30 litre of solution contains alcohol and water in the ratio 2:3. How ...
alcohol = 30*2/5 = 12 and water = 18 litres 
(12 + x)/(30 +x) = 60/100, we will get x = 15
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Most Upvoted Answer
30 litre of solution contains alcohol and water in the ratio 2:3. How ...
Understanding the Initial Solution
To solve the problem, we start with the initial 30 liters of solution that has alcohol and water in a ratio of 2:3.
- Total parts in the ratio = 2 + 3 = 5
- Alcohol in the solution = (2/5) * 30 liters = 12 liters
- Water in the solution = (3/5) * 30 liters = 18 liters
Target Concentration of Alcohol
We want to find out how much alcohol must be added to achieve a final solution that contains 60% alcohol.
- Let x be the amount of alcohol added.
- New volume of alcohol = 12 + x liters
- Total volume of the new solution = 30 + x liters
Setting Up the Equation
To find x, we set up the equation based on the desired concentration:
- The concentration of alcohol in the new solution is given by:
(12 + x) / (30 + x) = 60%
- Converting 60% to a fraction gives us:
(12 + x) / (30 + x) = 0.6
Solving the Equation
Cross-multiplying to eliminate the fraction:
- 12 + x = 0.6(30 + x)
- 12 + x = 18 + 0.6x
- Rearranging gives:
x - 0.6x = 18 - 12
- 0.4x = 6
- x = 6 / 0.4 = 15
Conclusion
Thus, the amount of alcohol that must be added to the solution to make it 60% alcohol is:
- 15 liters
The correct answer is option 'D'.
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