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A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
- a)4 : 1
- b)5 : 1
- c)16 : 9
- d)17 : 8
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken...
Given:
- A bottle contains 20 litres of liquid A.
- 4 litres of liquid A is taken out of it and replaced by the same quantity of liquid B.
- 4 litre of the mixture is taken out and replaced by the same quantity of liquid B.
To find: The ratio of the quantity of liquid A to that of liquid B in the final mixture.
Solution:
Let's assume that after n operations of replacement, the amount of liquid A left in the bottle is Aₙ and liquid B is Bₙ.
After the first operation of replacement:
- Quantity of liquid A left in the bottle = A₁ = 20 - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₁ = 4
After the second operation of replacement:
- Quantity of liquid A left in the bottle = A₂ = A₁ - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₂ = 4×(B/A)
We can write A₂ in terms of A₁ as follows:
A₂ = A₁ - 4 + 4×(B/A)
A₂ = (20 - 4 + 4×(B/A)) - 4 + 4×(B/A)
A₂ = A₁ - 4×(A/A) + 4×(B/A)
A₂ = A₁ + 4×(B/A) - 4
Similarly, we can write Bₙ in terms of A₁ as follows:
B₂ = 4×(B/A)
B₃ = 4×(B/A)×(B/A)
B₄ = 4×(B/A)×(B/A)×(B/A)
After n operations of replacement, we can write:
Aₙ = A₁ + 4×(B/A) - 4×(B/A)³
Bₙ = 4×(B/A)ⁿ
Substituting the values, we get:
Aₙ = 20×(1 - (1/5)³) + 4×(1 - (1/5)²)
Bₙ = 4×(1/5)ⁿ
Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is:
Aₙ:Bₙ = [20×(1 - (1/5)³) + 4×(1 - (1/5)²)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [16×(125/216) + 4×(16/25)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [100:27]:[1/5]ⁿ
Aₙ:Bₙ = 16:9 (n=2)
Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is 16:9.
- A bottle contains 20 litres of liquid A.
- 4 litres of liquid A is taken out of it and replaced by the same quantity of liquid B.
- 4 litre of the mixture is taken out and replaced by the same quantity of liquid B.
To find: The ratio of the quantity of liquid A to that of liquid B in the final mixture.
Solution:
Let's assume that after n operations of replacement, the amount of liquid A left in the bottle is Aₙ and liquid B is Bₙ.
After the first operation of replacement:
- Quantity of liquid A left in the bottle = A₁ = 20 - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₁ = 4
After the second operation of replacement:
- Quantity of liquid A left in the bottle = A₂ = A₁ - 4 + 4×(B/A)
- Quantity of liquid B in the bottle = B₂ = 4×(B/A)
We can write A₂ in terms of A₁ as follows:
A₂ = A₁ - 4 + 4×(B/A)
A₂ = (20 - 4 + 4×(B/A)) - 4 + 4×(B/A)
A₂ = A₁ - 4×(A/A) + 4×(B/A)
A₂ = A₁ + 4×(B/A) - 4
Similarly, we can write Bₙ in terms of A₁ as follows:
B₂ = 4×(B/A)
B₃ = 4×(B/A)×(B/A)
B₄ = 4×(B/A)×(B/A)×(B/A)
After n operations of replacement, we can write:
Aₙ = A₁ + 4×(B/A) - 4×(B/A)³
Bₙ = 4×(B/A)ⁿ
Substituting the values, we get:
Aₙ = 20×(1 - (1/5)³) + 4×(1 - (1/5)²)
Bₙ = 4×(1/5)ⁿ
Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is:
Aₙ:Bₙ = [20×(1 - (1/5)³) + 4×(1 - (1/5)²)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [16×(125/216) + 4×(16/25)]:[4×(1/5)ⁿ]
Aₙ:Bₙ = [100:27]:[1/5]ⁿ
Aₙ:Bₙ = 16:9 (n=2)
Therefore, the ratio of the quantity of liquid A to that of liquid B in the final mixture is 16:9.
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Community Answer
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken...
1. Initially 20ltrs of Liquid A, 4ltrs of Liquid A is removed, remaining quantity of A is 20-4=16.
2. Now same quantity of Liquid B is added i.e 4ltrs, now A:B=16:4=4:1(4/5 parts of A) & (1/5 parts of B).
3. 4ltrs of total mixture is removed, A=16-(4/5*4)=16-16/5=64/5 &
B= 4-(1/5*4)=4-4/5=16/5
After removal of 4ltrs of mixture remaining quantities in A and B are 64/5 and 16/5.
4. Now same quantity of Liquid B is replaced i.e is 4ltrs = (16/5)+4= 36/5.
5. Ratio of A and B is A:B or A/B = (64/5):(36/5)=16:9.
2. Now same quantity of Liquid B is added i.e 4ltrs, now A:B=16:4=4:1(4/5 parts of A) & (1/5 parts of B).
3. 4ltrs of total mixture is removed, A=16-(4/5*4)=16-16/5=64/5 &
B= 4-(1/5*4)=4-4/5=16/5
After removal of 4ltrs of mixture remaining quantities in A and B are 64/5 and 16/5.
4. Now same quantity of Liquid B is replaced i.e is 4ltrs = (16/5)+4= 36/5.
5. Ratio of A and B is A:B or A/B = (64/5):(36/5)=16:9.
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A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer?
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A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer?.
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?a)4 : 1b)5 : 1c)16 : 9d)17 : 8Correct answer is option 'C'. Can you explain this answer?.
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