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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?
Most Upvoted Answer
30 litre of solution contains alcohol and water in the ratio 2:3. How ...
Initial total volume = 30 L. Ratio alcohol:water = 2:3, so alcohol = 30 × 2/5 = 12 L.
Let x litres of alcohol be added. New alcohol = 12 + x. New total volume = 30 + x. Required fraction of alcohol = 60% = 3/5.
Set up the equation: (12 + x)/(30 + x) = 3/5.
Cross-multiply: 5(12 + x) = 3(30 + x).
60 + 5x = 90 + 3x ⇒ 5x − 3x = 90 − 60 ⇒ 2x = 30 ⇒ x = 15 L.
Therefore, 15 litres of alcohol must be added. (Option D)
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30 litre of solution contains alcohol and water in the ratio 2:3. How ...
Understanding the Initial Solution
The initial solution consists of 30 liters of liquid with alcohol and water in a 2:3 ratio. This means:
- Total parts: 2 (alcohol) + 3 (water) = 5 parts
- Alcohol volume: (2/5) * 30 liters = 12 liters
- Water volume: (3/5) * 30 liters = 18 liters
Calculating the Target Alcohol Concentration
We want to adjust this solution to have 60% alcohol. Let’s denote the amount of alcohol to be added as "x" liters. After adding "x" liters of alcohol, the new total volume of the solution will be:
- New total volume: 30 + x liters
The new volume of alcohol will be:
- New alcohol volume: 12 + x liters
To achieve a 60% alcohol concentration, we set up the following equation:
- (New alcohol volume) / (New total volume) = 60%
This translates to:
- (12 + x) / (30 + x) = 0.6
Solving the Equation
Now, we can cross-multiply to solve for x:
- 12 + x = 0.6 * (30 + x)
- 12 + x = 18 + 0.6x
- 12 + 0.4x = 18
- 0.4x = 18 - 12
- 0.4x = 6
- x = 6 / 0.4
- x = 15 liters
Conclusion
Therefore, to make the solution contain 60% alcohol, you must add 15 liters of alcohol. The correct answer is option D.
The initial solution consists of 30 liters of liquid with alcohol and water in a 2:3 ratio. This means:
- Total parts: 2 (alcohol) + 3 (water) = 5 parts
- Alcohol volume: (2/5) * 30 liters = 12 liters
- Water volume: (3/5) * 30 liters = 18 liters
Calculating the Target Alcohol Concentration
We want to adjust this solution to have 60% alcohol. Let’s denote the amount of alcohol to be added as "x" liters. After adding "x" liters of alcohol, the new total volume of the solution will be:
- New total volume: 30 + x liters
The new volume of alcohol will be:
- New alcohol volume: 12 + x liters
To achieve a 60% alcohol concentration, we set up the following equation:
- (New alcohol volume) / (New total volume) = 60%
This translates to:
- (12 + x) / (30 + x) = 0.6
Solving the Equation
Now, we can cross-multiply to solve for x:
- 12 + x = 0.6 * (30 + x)
- 12 + x = 18 + 0.6x
- 12 + 0.4x = 18
- 0.4x = 18 - 12
- 0.4x = 6
- x = 6 / 0.4
- x = 15 liters
Conclusion
Therefore, to make the solution contain 60% alcohol, you must add 15 liters of alcohol. The correct answer is option D.
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