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Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that x and y are co-prime?
- a)5
- b)9
- c)19
- d)21
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Solution A and solution B are 2 solutions of orange such that the conc...
The concentration of orange juice in solution A = 64%
The concentration of orange juice in solution B = 100-20 = 80%
The resultant solution obtained by mixing is of volume 20L out of which 6 L is water.
Quantity of orange juice = 20L - 6L =14L
Concentration of orange = 14/20 × 100% = 70%
As per question 0.64x + 0.8y = 0.7(x+y)
0.1y = 0.06x
x/y = 0.1/0.06 = 35
x = 5 and y = 3
3x + 2y = 3(5) + 2(3) = 15 + 6 = 21
Most Upvoted Answer
Solution A and solution B are 2 solutions of orange such that the conc...
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the ratio of solution A to solution B is x:y. Therefore, the total volume of solution A will be (20*x/(x+y)) liters, and the total volume of solution B will be (20*y/(x+y)) liters.
We are given that the concentration of orange juice in solution A is 64%. This means that 64% of the total volume of solution A is orange juice.
Therefore, the volume of orange juice in solution A is (0.64 * (20*x/(x+y))) liters.
Similarly, the concentration of water in solution B is 20%. This means that 20% of the total volume of solution B is water.
Therefore, the volume of water in solution B is (0.2 * (20*y/(x+y))) liters.
We are also given that the total solution has 6 liters of water. Therefore, we can set up the following equation:
(0.2 * (20*y/(x+y))) = 6
Simplifying this equation, we get:
(4*y/(x+y)) = 6
4y = 6(x+y)
4y = 6x + 6y
2y = 6x
Now, we need to find the value of 3x^2 + 2y^2. Since we know that 2y = 6x, we can substitute this value into the equation:
3x^2 + 2y^2 = 3x^2 + 2(6x)^2
= 3x^2 + 2(36x^2)
= 3x^2 + 72x^2
= 75x^2
Therefore, the value of 3x^2 + 2y^2 is 75x^2.
Since x and y are co-prime, we can find the value of 3x^2 + 2y^2 by substituting the value of y from the equation 2y = 6x:
3x^2 + 2(3x)^2 = 3x^2 + 18x^2 = 21x^2
Therefore, the value of 3x^2 + 2y^2 is 21x^2.
Hence, the correct answer is option D) 21.
Let's assume that the ratio of solution A to solution B is x:y. Therefore, the total volume of solution A will be (20*x/(x+y)) liters, and the total volume of solution B will be (20*y/(x+y)) liters.
We are given that the concentration of orange juice in solution A is 64%. This means that 64% of the total volume of solution A is orange juice.
Therefore, the volume of orange juice in solution A is (0.64 * (20*x/(x+y))) liters.
Similarly, the concentration of water in solution B is 20%. This means that 20% of the total volume of solution B is water.
Therefore, the volume of water in solution B is (0.2 * (20*y/(x+y))) liters.
We are also given that the total solution has 6 liters of water. Therefore, we can set up the following equation:
(0.2 * (20*y/(x+y))) = 6
Simplifying this equation, we get:
(4*y/(x+y)) = 6
4y = 6(x+y)
4y = 6x + 6y
2y = 6x
Now, we need to find the value of 3x^2 + 2y^2. Since we know that 2y = 6x, we can substitute this value into the equation:
3x^2 + 2y^2 = 3x^2 + 2(6x)^2
= 3x^2 + 2(36x^2)
= 3x^2 + 72x^2
= 75x^2
Therefore, the value of 3x^2 + 2y^2 is 75x^2.
Since x and y are co-prime, we can find the value of 3x^2 + 2y^2 by substituting the value of y from the equation 2y = 6x:
3x^2 + 2(3x)^2 = 3x^2 + 18x^2 = 21x^2
Therefore, the value of 3x^2 + 2y^2 is 21x^2.
Hence, the correct answer is option D) 21.
Community Answer
Solution A and solution B are 2 solutions of orange such that the conc...
Orange percentages :A : 64%B : 80% ( water % is given in question )Mixture : 70% ( from question 6L in 20L means 30% water ) Now A. B. 64. 80 70. 10. 6. = 10:6 = 5:3 ; x=5,Y=3 substitute in equation. Will get 21.
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Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer?
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Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. 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 Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer?.
Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. 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 Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer?.
Solutions for Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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ample number of questions to practice Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that xand yare co-prime?a)5b)9c)19d)21Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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