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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)11 litres
- b)5 litres
- c)6 litres
- d)8 litres
Correct answer is option 'A'. Can you explain this answer?
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:
Step 1: Calculate the amount of spirit and water in the first vessel
The ratio of spirit to water in the first vessel is 8:3, which means that for every 8 parts of spirit, there are 3 parts of water. Let's assume the amount of spirit in the first vessel is 8x and the amount of water is 3x.
Step 2: Calculate the amount of spirit and water in the second vessel
Similarly, the ratio of spirit to water in the second vessel is 5:1, so for every 5 parts of spirit, there is 1 part of water. Let's assume the amount of spirit in the second vessel is 5y and the amount of water is y.
Step 3: Determine the total amount of spirit and water in the two vessels
The total amount of spirit in the two vessels is 8x + 5y, and the total amount of water is 3x + y.
Step 4: Find the amount of mixture taken from the first vessel
Let's assume that x liters of mixture is taken from the first vessel.
Step 5: Calculate the amount of spirit and water in the mixture
Since the ratio of spirit to water in the mixture is 4:1, the amount of spirit in the mixture is 4x and the amount of water is x.
Step 6: Set up an equation based on the amount of spirit and water in the mixture
The amount of spirit in the mixture is equal to the amount of spirit in the first vessel, so we can write the equation: 4x = 8x + 5y.
Step 7: Solve the equation
Rearranging the equation, we get 4x - 8x = 5y, which simplifies to -4x = 5y.
Step 8: Calculate the amount of mixture taken from the first vessel
Since we need to find the amount of mixture taken from the first vessel (x), we can assume a value for y (e.g. y = 4) and solve for x.
Substituting y = 4 into the equation -4x = 5y, we get -4x = 5(4), which simplifies to -4x = 20.
Dividing both sides of the equation by -4, we get x = -5.
However, we cannot have a negative amount of mixture, so we need to consider another value for y. Let's try y = 8.
Substituting y = 8 into the equation -4x = 5y, we get -4x = 5(8), which simplifies to -4x = 40.
Dividing both sides of the equation by -4, we get x = -10.
Again, we cannot have a negative amount of mixture, so we need to consider another value for y. Let's try y = 12.
Substituting y = 12 into the equation -4x = 5y, we get -4x = 5(12), which simplifies to -4x = 60.
Dividing both sides of the equation by -4, we get x = -15.
Once again, we cannot have a negative amount of mixture, so we need to consider another value for y. Let
Step 1: Calculate the amount of spirit and water in the first vessel
The ratio of spirit to water in the first vessel is 8:3, which means that for every 8 parts of spirit, there are 3 parts of water. Let's assume the amount of spirit in the first vessel is 8x and the amount of water is 3x.
Step 2: Calculate the amount of spirit and water in the second vessel
Similarly, the ratio of spirit to water in the second vessel is 5:1, so for every 5 parts of spirit, there is 1 part of water. Let's assume the amount of spirit in the second vessel is 5y and the amount of water is y.
Step 3: Determine the total amount of spirit and water in the two vessels
The total amount of spirit in the two vessels is 8x + 5y, and the total amount of water is 3x + y.
Step 4: Find the amount of mixture taken from the first vessel
Let's assume that x liters of mixture is taken from the first vessel.
Step 5: Calculate the amount of spirit and water in the mixture
Since the ratio of spirit to water in the mixture is 4:1, the amount of spirit in the mixture is 4x and the amount of water is x.
Step 6: Set up an equation based on the amount of spirit and water in the mixture
The amount of spirit in the mixture is equal to the amount of spirit in the first vessel, so we can write the equation: 4x = 8x + 5y.
Step 7: Solve the equation
Rearranging the equation, we get 4x - 8x = 5y, which simplifies to -4x = 5y.
Step 8: Calculate the amount of mixture taken from the first vessel
Since we need to find the amount of mixture taken from the first vessel (x), we can assume a value for y (e.g. y = 4) and solve for x.
Substituting y = 4 into the equation -4x = 5y, we get -4x = 5(4), which simplifies to -4x = 20.
Dividing both sides of the equation by -4, we get x = -5.
However, we cannot have a negative amount of mixture, so we need to consider another value for y. Let's try y = 8.
Substituting y = 8 into the equation -4x = 5y, we get -4x = 5(8), which simplifies to -4x = 40.
Dividing both sides of the equation by -4, we get x = -10.
Again, we cannot have a negative amount of mixture, so we need to consider another value for y. Let's try y = 12.
Substituting y = 12 into the equation -4x = 5y, we get -4x = 5(12), which simplifies to -4x = 60.
Dividing both sides of the equation by -4, we get x = -15.
Once again, we cannot have a negative amount of mixture, so we need to consider another value for y. Let
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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.
In the first vessel, 8/11 th of the mixture is spirit; while in the second vessel, 5/6th of the mixture is spirit.
The spirit in the 35 litres cask is 4/5th of the mixture.
⇒ 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, 5/6th of the mixture is spirit.
The spirit in the 35 litres cask is 4/5th of the mixture.
⇒ X = 11
⇒ 11 litres of the mixture is taken from the first vessel.
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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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer?.
Solutions 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer?, a detailed solution 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of 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)11 litresb)5 litresc)6 litresd)8 litresCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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