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Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?
- a)18
- b)36
- c)27
- d)24
Correct answer is option 'D'. Can you explain this answer?
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Pipe A, B and C are kept open and together fill a tank in t minutes. P...
A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.
A and B together can fill 1t of the tank in a minute. A alone can fill 13t of the tank in a minute. So, in a minute, B can fill 1t−13t=23t. Or, B takes 3t2 minutes to fill an entire tank.
To fill one-third the tank, B will take t2 minutes. B is kept open for t - 10 minutes.
t2 = t - 10, t = 20 minutes.
A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes. Choice (D)
Most Upvoted Answer
Pipe A, B and C are kept open and together fill a tank in t minutes. P...
To find the value of t, the time taken to fill the tank completely, let's break down the problem step by step.
Given information:
- Pipe A is kept open throughout.
- Pipe B is kept open for the first 10 minutes and then closed.
- Pipe C is opened 2 minutes after pipe B is closed and is kept open till the tank is full.
- Each pipe fills an equal share of the tank.
1. Calculate the filling rate of each pipe:
Let the filling rate of each pipe be represented by the variables A, B, and C respectively.
Since the tank is filled in t minutes when all three pipes are open, the combined filling rate is 1/t.
The filling rate of pipe A is A.
The filling rate of pipe B is B.
The filling rate of pipe C is C.
2. Determine the filling rate of each pipe:
When pipe A and B are continuously open, the combined filling rate is 1/t.
The filling rate of pipe A is A.
The filling rate of pipe B is B.
3. Equate the filling rates:
Since the share filled by each pipe is equal, we can equate the filling rates:
A + B + C = 1/t ...(Equation 1)
4. Calculate the filling rate when pipe A and B are continuously open:
When pipe A and B are continuously open, the filling rate is A + B.
5. Determine the time taken to fill the tank when pipe A and B are continuously open:
Since the filling rate when pipe A and B are continuously open is A + B, the time taken to fill the tank completely is 1/(A + B).
6. Calculate the time taken to fill the tank when pipe A and B are continuously open:
Given that the time taken to fill the tank when pipe A and B are continuously open is t, we have:
1/(A + B) = t
Solving this equation for t, we get:
t = 1/(A + B) ...(Equation 2)
7. Substitute the value of t from Equation 2 into Equation 1:
Substituting the value of t from Equation 2 into Equation 1, we get:
A + B + C = 1/(1/(A + B))
Simplifying further, we get:
A + B + C = A + B
Canceling out A and B on both sides, we get:
C = 0
This implies that the filling rate of pipe C is 0, which means pipe C does not contribute to filling the tank.
8. Calculate the value of t:
Since pipe C does not contribute to filling the tank, we can ignore it in our calculations.
From Equation 2, we have:
t = 1/(A + B)
Since pipe A is kept open throughout, its filling rate is non-zero. Therefore, for t to be a finite value, pipe B must also have a non-zero filling rate.
The only option where t is finite is option (d) 24.
Given information:
- Pipe A is kept open throughout.
- Pipe B is kept open for the first 10 minutes and then closed.
- Pipe C is opened 2 minutes after pipe B is closed and is kept open till the tank is full.
- Each pipe fills an equal share of the tank.
1. Calculate the filling rate of each pipe:
Let the filling rate of each pipe be represented by the variables A, B, and C respectively.
Since the tank is filled in t minutes when all three pipes are open, the combined filling rate is 1/t.
The filling rate of pipe A is A.
The filling rate of pipe B is B.
The filling rate of pipe C is C.
2. Determine the filling rate of each pipe:
When pipe A and B are continuously open, the combined filling rate is 1/t.
The filling rate of pipe A is A.
The filling rate of pipe B is B.
3. Equate the filling rates:
Since the share filled by each pipe is equal, we can equate the filling rates:
A + B + C = 1/t ...(Equation 1)
4. Calculate the filling rate when pipe A and B are continuously open:
When pipe A and B are continuously open, the filling rate is A + B.
5. Determine the time taken to fill the tank when pipe A and B are continuously open:
Since the filling rate when pipe A and B are continuously open is A + B, the time taken to fill the tank completely is 1/(A + B).
6. Calculate the time taken to fill the tank when pipe A and B are continuously open:
Given that the time taken to fill the tank when pipe A and B are continuously open is t, we have:
1/(A + B) = t
Solving this equation for t, we get:
t = 1/(A + B) ...(Equation 2)
7. Substitute the value of t from Equation 2 into Equation 1:
Substituting the value of t from Equation 2 into Equation 1, we get:
A + B + C = 1/(1/(A + B))
Simplifying further, we get:
A + B + C = A + B
Canceling out A and B on both sides, we get:
C = 0
This implies that the filling rate of pipe C is 0, which means pipe C does not contribute to filling the tank.
8. Calculate the value of t:
Since pipe C does not contribute to filling the tank, we can ignore it in our calculations.
From Equation 2, we have:
t = 1/(A + B)
Since pipe A is kept open throughout, its filling rate is non-zero. Therefore, for t to be a finite value, pipe B must also have a non-zero filling rate.
The only option where t is finite is option (d) 24.
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Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?a)18b)36c)27d)24Correct answer is option 'D'. Can you explain this answer?
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Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?a)18b)36c)27d)24Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?a)18b)36c)27d)24Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?a)18b)36c)27d)24Correct answer is option 'D'. Can you explain this answer?.
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