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The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.
- a)8%, 16%, 32%
- b)27%, 9%, 3%
- c)12%, 24%, 48%
- d)44%, 22%, 11%
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The percentage amounts of an acid in three solutions form a geometric ...
Let's assume that the percentage amounts of acid in the first, second, and third solutions are a, ar, and ar^2 respectively, where a is the common ratio.
Let's analyze the first scenario where the solutions are mixed in the ratio 3:2:1 by weight. If we mix 3 parts of the first solution, 2 parts of the second solution, and 1 part of the third solution, the total weight of the resulting solution will be 3+2+1 = 6 parts.
Now, let's calculate the amount of acid in the resulting solution. Since the acid percentages form a geometric progression, we can write:
3a + 2ar + ar^2 = 0.22 * 6 (equation 1)
Simplifying equation 1, we get:
3a + 2ar + ar^2 = 1.32 (equation 2)
Similarly, in the second scenario where the solutions are mixed in the ratio 2:3:4 by weight, the total weight of the resulting solution is 2+3+4 = 9 parts. The amount of acid in this solution can be written as:
2a + 3ar + 4ar^2 = 0.32 * 9 (equation 3)
Simplifying equation 3, we get:
2a + 3ar + 4ar^2 = 2.88 (equation 4)
We now have a system of two equations (equations 2 and 4) with two variables (a and r). Let's solve this system to find the values of a and r.
By multiplying equation 2 by 2 and equation 4 by 3, we can eliminate the term 3ar and obtain a new equation:
6a + 4ar + 2ar^2 = 2.64 (equation 5)
6a + 9ar + 12ar^2 = 8.64 (equation 6)
By subtracting equation 5 from equation 6, we get:
5ar + 10ar^2 = 6 (equation 7)
Dividing equation 7 by 5, we have:
ar + 2ar^2 = 1.2 (equation 8)
Now, let's substitute equation 2 into equation 8:
1.32 + 2ar^2 = 1.2
2ar^2 = 1.2 - 1.32
2ar^2 = -0.12
ar^2 = -0.06
This equation has no real solutions, which means there is no unique solution for the acid percentages. Therefore, the given information is inconsistent, and it is not possible to determine the percentage of acid in each solution.
Let's analyze the first scenario where the solutions are mixed in the ratio 3:2:1 by weight. If we mix 3 parts of the first solution, 2 parts of the second solution, and 1 part of the third solution, the total weight of the resulting solution will be 3+2+1 = 6 parts.
Now, let's calculate the amount of acid in the resulting solution. Since the acid percentages form a geometric progression, we can write:
3a + 2ar + ar^2 = 0.22 * 6 (equation 1)
Simplifying equation 1, we get:
3a + 2ar + ar^2 = 1.32 (equation 2)
Similarly, in the second scenario where the solutions are mixed in the ratio 2:3:4 by weight, the total weight of the resulting solution is 2+3+4 = 9 parts. The amount of acid in this solution can be written as:
2a + 3ar + 4ar^2 = 0.32 * 9 (equation 3)
Simplifying equation 3, we get:
2a + 3ar + 4ar^2 = 2.88 (equation 4)
We now have a system of two equations (equations 2 and 4) with two variables (a and r). Let's solve this system to find the values of a and r.
By multiplying equation 2 by 2 and equation 4 by 3, we can eliminate the term 3ar and obtain a new equation:
6a + 4ar + 2ar^2 = 2.64 (equation 5)
6a + 9ar + 12ar^2 = 8.64 (equation 6)
By subtracting equation 5 from equation 6, we get:
5ar + 10ar^2 = 6 (equation 7)
Dividing equation 7 by 5, we have:
ar + 2ar^2 = 1.2 (equation 8)
Now, let's substitute equation 2 into equation 8:
1.32 + 2ar^2 = 1.2
2ar^2 = 1.2 - 1.32
2ar^2 = -0.12
ar^2 = -0.06
This equation has no real solutions, which means there is no unique solution for the acid percentages. Therefore, the given information is inconsistent, and it is not possible to determine the percentage of acid in each solution.
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The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage amounts of an acid in three solutions form a geometric progression. If we mix the first, second and third solutions in the ratio 3 : 2 : 1 by weight, we get a solution containing 22% acid. On the other hand, if we mix the solutions in the ratio 2 : 3 : 4 by weight, we obtain a solution containing 32% acid. Find the percentage of acid in each solution.a)8%, 16%, 32%b)27%, 9%, 3%c)12%, 24%, 48%d)44%, 22%, 11%e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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