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"A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"?
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"A solution contains a mixture of acid and base in the ratio 17 : 3. H...
Understanding the Problem
To solve the problem, we start with a mixture of acid and base in the ratio of 17:3. We need to determine how much of this mixture should be replaced with base such that the new ratio of acid to base becomes 1:1.
Initial Mixture Composition
- Let the total quantity of the mixture be 20 parts (17 parts acid + 3 parts base).
- Therefore, the initial amounts are:
- Acid = 17 parts
- Base = 3 parts
Let x be the fraction to be drawn off
- When we draw off x parts from the mixture, we remove:
- Acid removed = 17x/20
- Base removed = 3x/20
New Composition After Drawing Off x
- Remaining acid = 17 - (17x/20) = (340 - 17x)/20
- Remaining base = 3 - (3x/20) = (60 - 3x)/20
Substituting with Base
- After drawing off x parts, we add back x parts of base.
- New base amount = (60 - 3x)/20 + x = (60 - 3x + 20x)/20 = (60 + 17x)/20
Setting Up the Equation
- We want the new ratio of acid to base to be 1:1:
- (340 - 17x)/(60 + 17x) = 1
Solving the Equation
- Cross-multiplying gives us:
- 340 - 17x = 60 + 17x
- Rearranging yields: 280 = 34x
- Therefore, x = 280/34 = 40/5 = 8/5
Conclusion
To achieve a 1:1 ratio of acid and base, you must draw off 8/5 of the mixture and replace it entirely with base. Thus, the fraction of the mixture to be drawn off is 8/5 or 1.6 times the initial volume.
To solve the problem, we start with a mixture of acid and base in the ratio of 17:3. We need to determine how much of this mixture should be replaced with base such that the new ratio of acid to base becomes 1:1.
Initial Mixture Composition
- Let the total quantity of the mixture be 20 parts (17 parts acid + 3 parts base).
- Therefore, the initial amounts are:
- Acid = 17 parts
- Base = 3 parts
Let x be the fraction to be drawn off
- When we draw off x parts from the mixture, we remove:
- Acid removed = 17x/20
- Base removed = 3x/20
New Composition After Drawing Off x
- Remaining acid = 17 - (17x/20) = (340 - 17x)/20
- Remaining base = 3 - (3x/20) = (60 - 3x)/20
Substituting with Base
- After drawing off x parts, we add back x parts of base.
- New base amount = (60 - 3x)/20 + x = (60 - 3x + 20x)/20 = (60 + 17x)/20
Setting Up the Equation
- We want the new ratio of acid to base to be 1:1:
- (340 - 17x)/(60 + 17x) = 1
Solving the Equation
- Cross-multiplying gives us:
- 340 - 17x = 60 + 17x
- Rearranging yields: 280 = 34x
- Therefore, x = 280/34 = 40/5 = 8/5
Conclusion
To achieve a 1:1 ratio of acid and base, you must draw off 8/5 of the mixture and replace it entirely with base. Thus, the fraction of the mixture to be drawn off is 8/5 or 1.6 times the initial volume.
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"A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"?
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"A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about "A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for "A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"?.
"A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about "A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for "A solution contains a mixture of acid and base in the ratio 17 : 3. How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?"?.
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