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Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank in
- a)6 hours
- b)3 1/2 hours
- c)4 hours
- d)2 1/2 hours
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6...
Part of the tank filled by both pipes in two hours
Time taken by B in filling the remaining part
Time taken by B in filling the remaining part
Most Upvoted Answer
Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6...
Given:
Pipe A can fill the tank in 8 hours
Pipe B can fill the tank in 6 hours
To find:
Time taken by Pipe B to fill the remaining tank after Pipe A is closed after 2 hours.
Solution:
Let the capacity of the tank be C.
Pipe A can fill the tank in 8 hours. So, in 1 hour, Pipe A can fill 1/8th of the tank.
Similarly, Pipe B can fill the tank in 6 hours. So, in 1 hour, Pipe B can fill 1/6th of the tank.
Let's assume that both pipes are opened together and work for 2 hours. So, the amount of water filled in 2 hours will be:
Amount of water filled by Pipe A in 2 hours = 2 × 1/8 = 1/4th of the tank
Amount of water filled by Pipe B in 2 hours = 2 × 1/6 = 1/3rd of the tank
Total amount of water filled in 2 hours = 1/4 + 1/3 = 7/12th of the tank
After 2 hours, Pipe A is closed. So, Pipe B will have to fill the remaining tank capacity, which is:
Remaining capacity = 1 - 7/12 = 5/12th of the tank
Now, we need to find out the time taken by Pipe B to fill this remaining capacity.
Let's assume that Pipe B takes 'x' hours to fill the remaining 5/12th of the tank.
In 'x' hours, Pipe B can fill (1/6) × x of the tank.
According to the question, Pipe A was closed after 2 hours. So, the total time taken to fill the tank will be:
Total time taken = 2 + x
Total amount of water filled in this time = 1/4 + (1/6) × x
But we know that the total amount of water filled is equal to the capacity of the tank, which is C. So, we can write:
1/4 + (1/6) × x = C
Multiplying both sides by 12, we get:
3 + 2x = 12C
Simplifying, we get:
2x = 12C - 3
x = (12C - 3)/2
Now, we need to substitute the value of x in the expression for total time taken:
Total time taken = 2 + x
Total time taken = 2 + [(12C - 3)/2]
Total time taken = (4 + 12C - 3)/2
Total time taken = (12C + 1)/2
Therefore, the time taken by Pipe B to fill the remaining tank after Pipe A is closed after 2 hours is (12C + 1)/2 hours.
We know that the capacity of the tank is C. So, substituting C = 1, we get:
Time taken by Pipe B = (12 × 1 + 1)/2
Time taken by Pipe B = 13/2
Time taken by Pipe B = 6 1/2 hours
Rounding off to the nearest half hour, we get:
Time taken by Pipe B = 6 1/2 ≈ 7/2
Pipe A can fill the tank in 8 hours
Pipe B can fill the tank in 6 hours
To find:
Time taken by Pipe B to fill the remaining tank after Pipe A is closed after 2 hours.
Solution:
Let the capacity of the tank be C.
Pipe A can fill the tank in 8 hours. So, in 1 hour, Pipe A can fill 1/8th of the tank.
Similarly, Pipe B can fill the tank in 6 hours. So, in 1 hour, Pipe B can fill 1/6th of the tank.
Let's assume that both pipes are opened together and work for 2 hours. So, the amount of water filled in 2 hours will be:
Amount of water filled by Pipe A in 2 hours = 2 × 1/8 = 1/4th of the tank
Amount of water filled by Pipe B in 2 hours = 2 × 1/6 = 1/3rd of the tank
Total amount of water filled in 2 hours = 1/4 + 1/3 = 7/12th of the tank
After 2 hours, Pipe A is closed. So, Pipe B will have to fill the remaining tank capacity, which is:
Remaining capacity = 1 - 7/12 = 5/12th of the tank
Now, we need to find out the time taken by Pipe B to fill this remaining capacity.
Let's assume that Pipe B takes 'x' hours to fill the remaining 5/12th of the tank.
In 'x' hours, Pipe B can fill (1/6) × x of the tank.
According to the question, Pipe A was closed after 2 hours. So, the total time taken to fill the tank will be:
Total time taken = 2 + x
Total amount of water filled in this time = 1/4 + (1/6) × x
But we know that the total amount of water filled is equal to the capacity of the tank, which is C. So, we can write:
1/4 + (1/6) × x = C
Multiplying both sides by 12, we get:
3 + 2x = 12C
Simplifying, we get:
2x = 12C - 3
x = (12C - 3)/2
Now, we need to substitute the value of x in the expression for total time taken:
Total time taken = 2 + x
Total time taken = 2 + [(12C - 3)/2]
Total time taken = (4 + 12C - 3)/2
Total time taken = (12C + 1)/2
Therefore, the time taken by Pipe B to fill the remaining tank after Pipe A is closed after 2 hours is (12C + 1)/2 hours.
We know that the capacity of the tank is C. So, substituting C = 1, we get:
Time taken by Pipe B = (12 × 1 + 1)/2
Time taken by Pipe B = 13/2
Time taken by Pipe B = 6 1/2 hours
Rounding off to the nearest half hour, we get:
Time taken by Pipe B = 6 1/2 ≈ 7/2
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Community Answer
Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6...
Ans 10/4 aa rha h mera to.
a=8. 24. -3
b=6. -4.
2(3+4)=14. remaining work = 24-14 = 10
b do this work. 10/4 =5/2 days ans.
a=8. 24. -3
b=6. -4.
2(3+4)=14. remaining work = 24-14 = 10
b do this work. 10/4 =5/2 days ans.
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Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer?
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Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer?.
Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank ina)6 hoursb)3 1/2 hoursc)4 hoursd)2 1/2 hoursCorrect answer is option 'D'. Can you explain this answer?.
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