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A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?
Correct answer is '40'. Can you explain this answer?
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A solution has water and alcohol in the ratio 5 : 3. 16 litres of this...
Solution: Let the solution initially have 5x litres of water and 3x litres of alcohol.
16 litres of this solution (i.e., 10 litres of water and 6 litres of alcohol) is replaced by 16 litres of alcohol.
There are (5x - 10) litres of water and (3x + 10 ) litres of alcohol.
16 litres of this solution (i.e., 10 litres of water and 6 litres of alcohol) is replaced by 16 litres of alcohol.
There are (5x - 10) litres of water and (3x + 10 ) litres of alcohol.
X = 5
Quantity of the original solution = 3x + 5x = 8x = 40 litres
Answer: 40
Quantity of the original solution = 3x + 5x = 8x = 40 litres
Answer: 40
Most Upvoted Answer
A solution has water and alcohol in the ratio 5 : 3. 16 litres of this...
Given:
- The original solution has water and alcohol in the ratio 5:3.
- 16 liters of the original solution is replaced by 16 liters of alcohol.
- The resultant solution has water and alcohol in the ratio 3:5.
To find:
- The volume of the original solution.
Solution:
Let's assume that the original solution has a total volume of x liters.
Step 1: Calculating the water and alcohol content in the original solution
- The ratio of water to alcohol in the original solution is 5:3.
- This means for every 5 parts of water, there are 3 parts of alcohol.
- So, the amount of water in the original solution is (5/8) * x liters.
- And the amount of alcohol in the original solution is (3/8) * x liters.
Step 2: Calculating the water and alcohol content after replacement
- 16 liters of the original solution is replaced by 16 liters of alcohol.
- This means the amount of alcohol in the resultant solution is (3/8) * x + 16 liters.
- The amount of water in the resultant solution can be calculated by subtracting the alcohol content from the total volume of the resultant solution: x - [(3/8) * x + 16].
Step 3: Calculating the ratio of water to alcohol in the resultant solution
- The ratio of water to alcohol in the resultant solution is 3:5.
- This means for every 3 parts of water, there are 5 parts of alcohol.
- So, we can set up the following equation: (x - [(3/8) * x + 16]) / [(3/8) * x + 16] = 3/5.
Step 4: Solving the equation
- Simplifying the equation, we get: (8x - 3x - 128) / (3x + 128) = 3/5.
- Cross-multiplying, we get: 5(8x - 3x - 128) = 3(3x + 128).
- Simplifying further, we get: 40x - 15x - 640 = 9x + 384.
- Combining like terms, we get: 16x = 1024.
- Dividing both sides by 16, we get: x = 64.
Step 5: Finding the volume of the original solution
- The volume of the original solution is x liters, which is 64 liters.
Therefore, the volume of the original solution is 64 liters.
- The original solution has water and alcohol in the ratio 5:3.
- 16 liters of the original solution is replaced by 16 liters of alcohol.
- The resultant solution has water and alcohol in the ratio 3:5.
To find:
- The volume of the original solution.
Solution:
Let's assume that the original solution has a total volume of x liters.
Step 1: Calculating the water and alcohol content in the original solution
- The ratio of water to alcohol in the original solution is 5:3.
- This means for every 5 parts of water, there are 3 parts of alcohol.
- So, the amount of water in the original solution is (5/8) * x liters.
- And the amount of alcohol in the original solution is (3/8) * x liters.
Step 2: Calculating the water and alcohol content after replacement
- 16 liters of the original solution is replaced by 16 liters of alcohol.
- This means the amount of alcohol in the resultant solution is (3/8) * x + 16 liters.
- The amount of water in the resultant solution can be calculated by subtracting the alcohol content from the total volume of the resultant solution: x - [(3/8) * x + 16].
Step 3: Calculating the ratio of water to alcohol in the resultant solution
- The ratio of water to alcohol in the resultant solution is 3:5.
- This means for every 3 parts of water, there are 5 parts of alcohol.
- So, we can set up the following equation: (x - [(3/8) * x + 16]) / [(3/8) * x + 16] = 3/5.
Step 4: Solving the equation
- Simplifying the equation, we get: (8x - 3x - 128) / (3x + 128) = 3/5.
- Cross-multiplying, we get: 5(8x - 3x - 128) = 3(3x + 128).
- Simplifying further, we get: 40x - 15x - 640 = 9x + 384.
- Combining like terms, we get: 16x = 1024.
- Dividing both sides by 16, we get: x = 64.
Step 5: Finding the volume of the original solution
- The volume of the original solution is x liters, which is 64 liters.
Therefore, the volume of the original solution is 64 liters.
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A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer?
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A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. 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 A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer?.
A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. 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 A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer?.
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A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer?, a detailed solution for A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer? has been provided alongside types of A solution has water and alcohol in the ratio 5 : 3. 16 litres of this solution is replaced by 16 litres of alcohol. The resultant solution has water and alcohol in the ratio 3 : 5. What is the volume (in litres) of the original solution?Correct answer is '40'. Can you explain this answer? theory, EduRev gives you an
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