UPSC Exam > UPSC Questions > A bottle contains 20 litres of liquid A. 4 li...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
Free Test
FREE
| Start Free Test |
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.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup