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A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?
- a)24 litres
- b)21 litres
- c)18 litres
- d)27 litres
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A vessel contains a mixture of two liquids A and B in the ratio of 7:5...
Let 7x and 5x volume of liquids A and Liquid B are present in vessel then,
Hence, 7.3 = 211 liquid A was present.
Most Upvoted Answer
A vessel contains a mixture of two liquids A and B in the ratio of 7:5...
Given:
- Initially, the ratio of A and B in the mixture = 7:5
- 9 litres of the mixture is taken out and replaced with B
- After the replacement, the ratio of A and B in the mixture = 7:9
To Find: The initial quantity of liquid A in the vessel
Solution:
Let's assume that the initial quantity of the mixture in the vessel is 12x litres (7x litres of liquid A and 5x litres of liquid B).
Step 1: Calculation before replacement
- Initially, A:B = 7:5, so the quantity of A and B in the mixture would be 7x and 5x respectively.
- Therefore, the total quantity of the mixture in the vessel = 7x + 5x = 12x litres
Step 2: Calculation after replacement
- 9 litres of the mixture is taken out, so the quantity of the mixture left in the vessel = 12x - 9 litres
- This quantity is then filled with B. Let's assume that y litres of B is added to the mixture to fill the vessel
- Now, the quantity of B in the mixture = 5x + y litres, and the quantity of A in the mixture = 7x litres
- As per the question, the ratio of A and B in the mixture after replacement = 7:9, so we can form an equation as follows:
7x/(5x+y) = 7/9
- Cross-multiplying, we get:
63x = 35x + 9y
- Simplifying, we get:
28x = 9y
Step 3: Solving the equations
- We have two equations now:
12x - 9 = 5x + y (from step 2)
28x = 9y (from step 2)
- Solving these equations simultaneously, we get:
x = 3, y = 28
- Therefore, the initial quantity of liquid A in the vessel = 7x = 21 litres
Final Answer: The initial quantity of liquid A in the vessel was 21 litres. Hence, option (b) is the correct answer.
- Initially, the ratio of A and B in the mixture = 7:5
- 9 litres of the mixture is taken out and replaced with B
- After the replacement, the ratio of A and B in the mixture = 7:9
To Find: The initial quantity of liquid A in the vessel
Solution:
Let's assume that the initial quantity of the mixture in the vessel is 12x litres (7x litres of liquid A and 5x litres of liquid B).
Step 1: Calculation before replacement
- Initially, A:B = 7:5, so the quantity of A and B in the mixture would be 7x and 5x respectively.
- Therefore, the total quantity of the mixture in the vessel = 7x + 5x = 12x litres
Step 2: Calculation after replacement
- 9 litres of the mixture is taken out, so the quantity of the mixture left in the vessel = 12x - 9 litres
- This quantity is then filled with B. Let's assume that y litres of B is added to the mixture to fill the vessel
- Now, the quantity of B in the mixture = 5x + y litres, and the quantity of A in the mixture = 7x litres
- As per the question, the ratio of A and B in the mixture after replacement = 7:9, so we can form an equation as follows:
7x/(5x+y) = 7/9
- Cross-multiplying, we get:
63x = 35x + 9y
- Simplifying, we get:
28x = 9y
Step 3: Solving the equations
- We have two equations now:
12x - 9 = 5x + y (from step 2)
28x = 9y (from step 2)
- Solving these equations simultaneously, we get:
x = 3, y = 28
- Therefore, the initial quantity of liquid A in the vessel = 7x = 21 litres
Final Answer: The initial quantity of liquid A in the vessel was 21 litres. Hence, option (b) is the correct answer.
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A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer?
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A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer?.
A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel contains a mixture of two liquids A and B in the ratio of 7:5. When 9 litres of the mixture is taken out and the vessel is filled with B, the ratio of A and B is now 7:9. How many litres of liquid A was there in the vessel initially?a)24 litresb)21 litresc)18 litresd)27 litresCorrect answer is option 'B'. Can you explain this answer?.
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