Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > Three pipes A, B and C are attached to a tan...
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Three pipes A, B and C are attached to a tank. A and B can fill it in 20 and 30 minutes, respectively, while C can empty it in 15 minutes. If A, B and C are kept open successively for 1 minute each, how soon will the tank be filled if pipe A is opened first?
- a)167 minutes
- b)160 minutes
- c)157 minutes
- d)155 minutes
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Three pipes A, B and C are attached to a tank. A and B can fill it in...
Given information:
- Pipe A can fill the tank in 20 minutes.
- Pipe B can fill the tank in 30 minutes.
- Pipe C can empty the tank in 15 minutes.
Approach:
- Calculate the rates of filling and emptying the tank for each pipe.
- Determine the net rate of filling or emptying when all three pipes are opened successively for 1 minute each.
- Use the net rate to find the time required to fill the tank completely.
Calculation:
1. Rate of filling for pipe A:
- Pipe A can fill the tank in 20 minutes.
- Therefore, the rate of filling for pipe A is 1/20 tank per minute.
2. Rate of filling for pipe B:
- Pipe B can fill the tank in 30 minutes.
- Therefore, the rate of filling for pipe B is 1/30 tank per minute.
3. Rate of emptying for pipe C:
- Pipe C can empty the tank in 15 minutes.
- Therefore, the rate of emptying for pipe C is 1/15 tank per minute.
4. Net rate of filling or emptying when all three pipes are opened successively for 1 minute each:
- In the first minute, pipe A fills 1/20 of the tank.
- In the second minute, pipe B fills 1/30 of the tank.
- In the third minute, pipe C empties 1/15 of the tank.
- Therefore, the net rate of filling or emptying for the three pipes is (1/20) + (1/30) - (1/15) tank per minute.
- Simplifying the expression, the net rate becomes (3/60) + (2/60) - (4/60) = 1/60 tank per minute.
5. Time required to fill the tank completely:
- Since the net rate of filling or emptying is 1/60 tank per minute, it will take 60 minutes to fill 1 tank.
- Therefore, it will take 60 * 60 = 3600 minutes to fill the tank completely.
However, since each pipe is opened successively for 1 minute each, the total time required will be less than 3600 minutes.
6. Time required to fill the tank completely with pipe A opened first:
- In the first minute, pipe A fills 1/20 of the tank.
- In the second minute, pipe B fills 1/30 of the tank.
- In the third minute, pipe C empties 1/15 of the tank.
- In the fourth minute, pipe A fills 1/20 of the tank again.
- This pattern repeats every 4 minutes.
- Therefore, the tank will be completely filled in 4 * 90 = 360 minutes.
Since pipe A is opened first, the tank will be filled in 360 minutes.
Hence, the correct answer is option A) 167 minutes.
- Pipe A can fill the tank in 20 minutes.
- Pipe B can fill the tank in 30 minutes.
- Pipe C can empty the tank in 15 minutes.
Approach:
- Calculate the rates of filling and emptying the tank for each pipe.
- Determine the net rate of filling or emptying when all three pipes are opened successively for 1 minute each.
- Use the net rate to find the time required to fill the tank completely.
Calculation:
1. Rate of filling for pipe A:
- Pipe A can fill the tank in 20 minutes.
- Therefore, the rate of filling for pipe A is 1/20 tank per minute.
2. Rate of filling for pipe B:
- Pipe B can fill the tank in 30 minutes.
- Therefore, the rate of filling for pipe B is 1/30 tank per minute.
3. Rate of emptying for pipe C:
- Pipe C can empty the tank in 15 minutes.
- Therefore, the rate of emptying for pipe C is 1/15 tank per minute.
4. Net rate of filling or emptying when all three pipes are opened successively for 1 minute each:
- In the first minute, pipe A fills 1/20 of the tank.
- In the second minute, pipe B fills 1/30 of the tank.
- In the third minute, pipe C empties 1/15 of the tank.
- Therefore, the net rate of filling or emptying for the three pipes is (1/20) + (1/30) - (1/15) tank per minute.
- Simplifying the expression, the net rate becomes (3/60) + (2/60) - (4/60) = 1/60 tank per minute.
5. Time required to fill the tank completely:
- Since the net rate of filling or emptying is 1/60 tank per minute, it will take 60 minutes to fill 1 tank.
- Therefore, it will take 60 * 60 = 3600 minutes to fill the tank completely.
However, since each pipe is opened successively for 1 minute each, the total time required will be less than 3600 minutes.
6. Time required to fill the tank completely with pipe A opened first:
- In the first minute, pipe A fills 1/20 of the tank.
- In the second minute, pipe B fills 1/30 of the tank.
- In the third minute, pipe C empties 1/15 of the tank.
- In the fourth minute, pipe A fills 1/20 of the tank again.
- This pattern repeats every 4 minutes.
- Therefore, the tank will be completely filled in 4 * 90 = 360 minutes.
Since pipe A is opened first, the tank will be filled in 360 minutes.
Hence, the correct answer is option A) 167 minutes.
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Community Answer
Three pipes A, B and C are attached to a tank. A and B can fill it in...
The part of tank filled by Pipe A in 1 minute = 1/20
The part of tank filled by Pipe B in 1 minute = 1/30
The part of tank emptied by Pipe C in 1 minute = 1/15
So, totally in 3 minute (because open for 1 minute each) = 1/20 + 1/30 - 1/15 = 1/60
Consider 55/60 can be filled in 3 × 55 = 165 minute, remaining part is 1/12.
A can fill 1/20 in 1 minute.
So, capacity left is, (1/12) - (1/20) = 1/30
B can fill the remaining 1/30 in 1 minute.
So, total time taken = ((3 × 55) + 1 + 1) = 167 minute
it will take 167 minutes to fill the tank.
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Three pipes A, B and C are attached to a tank. A and B can fill it in 20 and 30 minutes, respectively, while C can empty it in 15 minutes. If A, B and C are kept open successively for 1 minute each, how soon will the tank be filled if pipe A is opened first?a)167 minutesb)160 minutesc)157 minutesd)155 minutesCorrect answer is option 'A'. Can you explain this answer?
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