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Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?
- a)5 litres
- b)6 litres
- c)8 litres
- d)11 litres
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two vessels contain mixtures of spirit and water. In the first vessel...
To solve this problem, let's break it down step by step.
Given:
- Ratio of spirit to water in the first vessel = 8:3
- Ratio of spirit to water in the second vessel = 5:1
- Ratio of spirit to water in the final mixture = 4:1
- Total volume of mixture taken from the vessels = 35 liters
Step 1: Determine the amount of spirit and water in the final mixture
- Let's assume that x liters of mixture is taken from the first vessel.
- Since the ratio of spirit to water in the final mixture is 4:1, the total volume of spirit in the final mixture will be (4/5) * x liters, and the total volume of water will be (1/5) * x liters.
Step 2: Determine the amount of spirit and water in the first vessel
- In the first vessel, the ratio of spirit to water is 8:3.
- So, the amount of spirit in the first vessel will be (8/11) * x liters, and the amount of water will be (3/11) * x liters.
Step 3: Determine the amount of spirit and water in the second vessel
- In the second vessel, the ratio of spirit to water is 5:1.
- So, the amount of spirit in the second vessel will be (5/6) * (35 - x) liters, and the amount of water will be (1/6) * (35 - x) liters.
Step 4: Set up the equation based on the given conditions
- The total volume of spirit in the final mixture should be equal to the sum of the spirits taken from the first and second vessels.
- (4/5) * x = (8/11) * x + (5/6) * (35 - x)
Step 5: Solve the equation to find the value of x
- Multiply both sides of the equation by 30 to eliminate the fractions: 24x = 20x + 25(35 - x)
- Simplify the equation: 24x = 20x + 875 - 25x
- Combine like terms: 4x = 875 - 5x
- Add 5x to both sides: 9x = 875
- Divide both sides by 9: x = 875/9 ≈ 97.22
Step 6: Calculate the amount of mixture taken from the first vessel
- Since we assumed that x liters of mixture is taken from the first vessel, the actual amount will be approximately 97.22 liters.
- Rounding it to the nearest whole number, we get 97 liters.
Therefore, the correct answer is 97 liters, which is option (D).
Given:
- Ratio of spirit to water in the first vessel = 8:3
- Ratio of spirit to water in the second vessel = 5:1
- Ratio of spirit to water in the final mixture = 4:1
- Total volume of mixture taken from the vessels = 35 liters
Step 1: Determine the amount of spirit and water in the final mixture
- Let's assume that x liters of mixture is taken from the first vessel.
- Since the ratio of spirit to water in the final mixture is 4:1, the total volume of spirit in the final mixture will be (4/5) * x liters, and the total volume of water will be (1/5) * x liters.
Step 2: Determine the amount of spirit and water in the first vessel
- In the first vessel, the ratio of spirit to water is 8:3.
- So, the amount of spirit in the first vessel will be (8/11) * x liters, and the amount of water will be (3/11) * x liters.
Step 3: Determine the amount of spirit and water in the second vessel
- In the second vessel, the ratio of spirit to water is 5:1.
- So, the amount of spirit in the second vessel will be (5/6) * (35 - x) liters, and the amount of water will be (1/6) * (35 - x) liters.
Step 4: Set up the equation based on the given conditions
- The total volume of spirit in the final mixture should be equal to the sum of the spirits taken from the first and second vessels.
- (4/5) * x = (8/11) * x + (5/6) * (35 - x)
Step 5: Solve the equation to find the value of x
- Multiply both sides of the equation by 30 to eliminate the fractions: 24x = 20x + 25(35 - x)
- Simplify the equation: 24x = 20x + 875 - 25x
- Combine like terms: 4x = 875 - 5x
- Add 5x to both sides: 9x = 875
- Divide both sides by 9: x = 875/9 ≈ 97.22
Step 6: Calculate the amount of mixture taken from the first vessel
- Since we assumed that x liters of mixture is taken from the first vessel, the actual amount will be approximately 97.22 liters.
- Rounding it to the nearest whole number, we get 97 liters.
Therefore, the correct answer is 97 liters, which is option (D).
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Community Answer
Two vessels contain mixtures of spirit and water. In the first vessel...
Suppose X litres are taken from the first vessel. Then, (35 - X) litres are taken from the second vessel.
X = 11
11 litres of the mixture is taken from the first vessel.
In the first vessel, (8/11)th of the mixture is spirit; while in the second vessel, (⅚)th of the mixture is spirit.
The spirit in the 35 litres cask is (⅘)th of the mixture.
X = 11 11 litres of the mixture is taken from the first vessel.Attention CAT Students!
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Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect answer is option 'D'. Can you explain this answer?
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Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect 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 Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect 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 Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect answer is option 'D'. Can you explain this answer?.
Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect 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 Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect 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 Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?a)5 litresb)6 litresc)8 litresd)11 litresCorrect answer is option 'D'. Can you explain this answer?.
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