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A 650 ml solution has 25% alcohol. How much alcohol must be mixed with the solution so that the resultant mixture has 35% alcohol?
- a)50 ml
- b)75 ml
- c)100 ml
- d)150 ml
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Problem
To solve the problem, we need to determine how much alcohol must be added to a 650 ml solution that has 25% alcohol to achieve a final concentration of 35%.
Initial Alcohol Content
- The initial solution has a volume of 650 ml.
- The concentration of alcohol is 25%.
Calculating the initial amount of alcohol:
- Initial amount of alcohol = 25% of 650 ml
- Initial amount of alcohol = 0.25 * 650 = 162.5 ml
Final Concentration Requirement
- Let "x" be the amount of alcohol to be added.
- After adding x ml of alcohol, the total volume of the solution becomes (650 + x) ml.
- The new alcohol content will be (162.5 + x) ml.
We want the final solution to have a concentration of 35%, so we set up the equation:
- (162.5 + x) / (650 + x) = 35%
Solve the Equation
1. Cross-multiply to eliminate the fraction:
- 162.5 + x = 0.35 * (650 + x)
2. Distributing:
- 162.5 + x = 227.5 + 0.35x
3. Rearranging:
- 162.5 + x - 0.35x = 227.5
- 0.65x = 227.5 - 162.5
- 0.65x = 65
4. Solving for x:
- x = 65 / 0.65
- x = 100 ml
Conclusion
To achieve a 35% alcohol concentration, you need to add 100 ml of alcohol to the original solution. Thus, the correct answer is option C.
To solve the problem, we need to determine how much alcohol must be added to a 650 ml solution that has 25% alcohol to achieve a final concentration of 35%.
Initial Alcohol Content
- The initial solution has a volume of 650 ml.
- The concentration of alcohol is 25%.
Calculating the initial amount of alcohol:
- Initial amount of alcohol = 25% of 650 ml
- Initial amount of alcohol = 0.25 * 650 = 162.5 ml
Final Concentration Requirement
- Let "x" be the amount of alcohol to be added.
- After adding x ml of alcohol, the total volume of the solution becomes (650 + x) ml.
- The new alcohol content will be (162.5 + x) ml.
We want the final solution to have a concentration of 35%, so we set up the equation:
- (162.5 + x) / (650 + x) = 35%
Solve the Equation
1. Cross-multiply to eliminate the fraction:
- 162.5 + x = 0.35 * (650 + x)
2. Distributing:
- 162.5 + x = 227.5 + 0.35x
3. Rearranging:
- 162.5 + x - 0.35x = 227.5
- 0.65x = 227.5 - 162.5
- 0.65x = 65
4. Solving for x:
- x = 65 / 0.65
- x = 100 ml
Conclusion
To achieve a 35% alcohol concentration, you need to add 100 ml of alcohol to the original solution. Thus, the correct answer is option C.
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Question Description
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