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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 ...
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
Hence, it will take 167 minutes to fill the tank.
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
Hence, it will take 167 minutes to fill the tank.
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Community Answer
Three pipes A, B and C are attached to a tank. A and B can fill it in ...
Given:
- 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:
1. Let's calculate the rates at which each pipe fills or empties the tank.
2. Then we'll determine how much the tank fills or empties in 1 minute.
3. Finally, we'll keep the pipes open successively for 1 minute each and calculate the time it takes to fill the tank.
Calculations:
- Pipe A fills the tank in 20 minutes, so its filling rate is 1/20th of the tank per minute.
- Pipe B fills the tank in 30 minutes, so its filling rate is 1/30th of the tank per minute.
- Pipe C empties the tank in 15 minutes, so its emptying rate is 1/15th of the tank per minute.
In 1 minute:
- Pipe A fills 1/20th of the tank.
- Pipe B fills 1/30th of the tank.
- Pipe C empties 1/15th of the tank.
Let's calculate the net effect of keeping the pipes open successively for 1 minute each:
- First minute: Pipe A fills 1/20th of the tank.
- Second minute: Pipe B fills 1/30th of the tank, and the total filled is 1/20 + 1/30 = 1/12th of the tank.
- Third minute: Pipe C empties 1/15th of the tank, and the total filled is 1/12 - 1/15 = 1/20th of the tank.
Observation:
- After every 3 minutes, 1/20th of the tank is filled.
Calculation of time to fill the tank:
- Since we are filling 1/20th of the tank in 3 minutes, to fill the entire tank, it will take 20 * 3 = 60 minutes.
Answer:
- However, we need to keep in mind that we started with pipe A open for the first minute.
- So, the time taken to fill the tank completely will be 60 + 1 = 61 minutes.
Therefore, 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:
1. Let's calculate the rates at which each pipe fills or empties the tank.
2. Then we'll determine how much the tank fills or empties in 1 minute.
3. Finally, we'll keep the pipes open successively for 1 minute each and calculate the time it takes to fill the tank.
Calculations:
- Pipe A fills the tank in 20 minutes, so its filling rate is 1/20th of the tank per minute.
- Pipe B fills the tank in 30 minutes, so its filling rate is 1/30th of the tank per minute.
- Pipe C empties the tank in 15 minutes, so its emptying rate is 1/15th of the tank per minute.
In 1 minute:
- Pipe A fills 1/20th of the tank.
- Pipe B fills 1/30th of the tank.
- Pipe C empties 1/15th of the tank.
Let's calculate the net effect of keeping the pipes open successively for 1 minute each:
- First minute: Pipe A fills 1/20th of the tank.
- Second minute: Pipe B fills 1/30th of the tank, and the total filled is 1/20 + 1/30 = 1/12th of the tank.
- Third minute: Pipe C empties 1/15th of the tank, and the total filled is 1/12 - 1/15 = 1/20th of the tank.
Observation:
- After every 3 minutes, 1/20th of the tank is filled.
Calculation of time to fill the tank:
- Since we are filling 1/20th of the tank in 3 minutes, to fill the entire tank, it will take 20 * 3 = 60 minutes.
Answer:
- However, we need to keep in mind that we started with pipe A open for the first minute.
- So, the time taken to fill the tank completely will be 60 + 1 = 61 minutes.
Therefore, the correct answer is option 'A' - 167 minutes.
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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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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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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