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The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1?
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The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form...
Given information:
- The percentage volumes of liquor in 3 cocktails - C1, C2, and C3 - form a geometric progression in that order.
- When we mix the 1st drink, the 2nd drink, and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor.
- When we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor.
Assumptions:
- Let the percentage volumes of liquor in C1, C2, and C3 be a, ar, and ar^2 respectively, where r is the common ratio.
Deriving the equations:
- According to the given information, when we mix the drinks in the ratio 2 : 3 : 4, the percentage of liquor in the resulting drink is 32%. This can be expressed as:
(2a + 3ar + 4ar^2) / (2 + 3 + 4) = 32
Simplifying, we get:
2a + 3ar + 4ar^2 = 32 * 9
2a + 3ar + 4ar^2 = 288 -- Equation 1
- Similarly, when we mix the drinks in the ratio 3 : 2 : 1, the percentage of liquor in the resulting drink is 22%. This can be expressed as:
(3a + 2ar + ar^2) / (3 + 2 + 1) = 22
Simplifying, we get:
3a + 2ar + ar^2 = 22 * 6
3a + 2ar + ar^2 = 132 -- Equation 2
Solving the equations:
- We have two equations, Equation 1 and Equation 2, with two variables a and r. We can solve these equations simultaneously to find their values.
- Subtracting Equation 2 from Equation 1, we get:
(2a + 3ar + 4ar^2) - (3a + 2ar + ar^2) = 288 - 132
Simplifying, we get:
-a + 2ar + 3ar^2 = 156 -- Equation 3
- Rearranging Equation 3, we get:
3ar^2 + 2ar - a = 156 -- Equation 4
- We can rewrite Equation 4 in the form of a quadratic equation:
3ar^2 + 2ar - a - 156 = 0
- To solve this quadratic equation, we can use the quadratic formula:
r = (-b ± √(b^2 - 4ac)) / (2a)
- Plugging in the values from Equation 4, we get:
a = 3, b = 2, c = -156
- Solving the quadratic equation, we find two possible values for r: r = 4 or r = -13/3
Final calculation:
- Since
- The percentage volumes of liquor in 3 cocktails - C1, C2, and C3 - form a geometric progression in that order.
- When we mix the 1st drink, the 2nd drink, and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor.
- When we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor.
Assumptions:
- Let the percentage volumes of liquor in C1, C2, and C3 be a, ar, and ar^2 respectively, where r is the common ratio.
Deriving the equations:
- According to the given information, when we mix the drinks in the ratio 2 : 3 : 4, the percentage of liquor in the resulting drink is 32%. This can be expressed as:
(2a + 3ar + 4ar^2) / (2 + 3 + 4) = 32
Simplifying, we get:
2a + 3ar + 4ar^2 = 32 * 9
2a + 3ar + 4ar^2 = 288 -- Equation 1
- Similarly, when we mix the drinks in the ratio 3 : 2 : 1, the percentage of liquor in the resulting drink is 22%. This can be expressed as:
(3a + 2ar + ar^2) / (3 + 2 + 1) = 22
Simplifying, we get:
3a + 2ar + ar^2 = 22 * 6
3a + 2ar + ar^2 = 132 -- Equation 2
Solving the equations:
- We have two equations, Equation 1 and Equation 2, with two variables a and r. We can solve these equations simultaneously to find their values.
- Subtracting Equation 2 from Equation 1, we get:
(2a + 3ar + 4ar^2) - (3a + 2ar + ar^2) = 288 - 132
Simplifying, we get:
-a + 2ar + 3ar^2 = 156 -- Equation 3
- Rearranging Equation 3, we get:
3ar^2 + 2ar - a = 156 -- Equation 4
- We can rewrite Equation 4 in the form of a quadratic equation:
3ar^2 + 2ar - a - 156 = 0
- To solve this quadratic equation, we can use the quadratic formula:
r = (-b ± √(b^2 - 4ac)) / (2a)
- Plugging in the values from Equation 4, we get:
a = 3, b = 2, c = -156
- Solving the quadratic equation, we find two possible values for r: r = 4 or r = -13/3
Final calculation:
- Since
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The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ?
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The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ? 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 volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ?.
The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ? 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 volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage volumes of liquor in 3 cocktails - C1, C2 and C3 - form a geometric progression in that order. If we mix the 1st drink, the 2nd drink and the 3rd drink respectively in the ratio 2 : 3 : 4, we obtain a drink with 32% liquor. If we mix them in the ratio 3 : 2 : 1, we obtain a drink with 22% liquor. What is the percentage of liquor in C1? ?.
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