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Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?
- a)6 hrs 40 minutes
- b)8 hrs 30 minutes
- c)7 hrs 30 minutes
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respective...
Since tank B is two times the volume of tank A so pipe R will take 20 hrs to empty Tank A. When all the three pipes are connected to tank R then in one hour, water filled = 
Hence it will take 15/2 hours or 7 hours 30 minutes to fill the tank.
Most Upvoted Answer
Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respective...
Given:
- Pipe P fills tank A in 10 hours
- Pipe Q fills tank A in 12 hours
- Pipe R empties tank B in 40 hours
- Tank B is twice the volume of tank A
To find:
- How long it will take to fill tank A when pipes P and Q are open to fill it and pipe R is connected to empty it at the same time
Let's calculate the rates at which each pipe fills or empties the tanks:
- Pipe P fills tank A in 10 hours, so its filling rate is 1/10 of the tank per hour
- Pipe Q fills tank A in 12 hours, so its filling rate is 1/12 of the tank per hour
- Pipe R empties tank B in 40 hours, so its emptying rate is 1/40 of the tank per hour
Since tank B is twice the volume of tank A, the emptying rate of pipe R is twice the filling rates of pipes P and Q. Therefore, we can conclude that the effective emptying rate of pipe R is (1/10 + 1/12) - (1/40) = 11/120 of the tank per hour.
To find the time it takes to fill tank A, we need to calculate the net filling rate when all three pipes are operating simultaneously:
Net filling rate = Filling rate of pipes P and Q - Emptying rate of pipe R
= (1/10 + 1/12) - (11/120)
= 12/120 + 10/120 - 11/120
= 11/120
Therefore, the net filling rate is 11/120 of the tank per hour.
Now, let's calculate the time it takes to fill tank A:
Tank A = 1 unit
Net filling rate = 11/120 of the tank per hour
Time taken to fill tank A = 1 / (11/120) hours
= 120/11 hours
= 10 hours and 54 minutes
Since the options given are in hours and minutes, we can round up the time to the nearest hour and minute, which is 11 hours.
- Pipe P fills tank A in 10 hours
- Pipe Q fills tank A in 12 hours
- Pipe R empties tank B in 40 hours
- Tank B is twice the volume of tank A
To find:
- How long it will take to fill tank A when pipes P and Q are open to fill it and pipe R is connected to empty it at the same time
Let's calculate the rates at which each pipe fills or empties the tanks:
- Pipe P fills tank A in 10 hours, so its filling rate is 1/10 of the tank per hour
- Pipe Q fills tank A in 12 hours, so its filling rate is 1/12 of the tank per hour
- Pipe R empties tank B in 40 hours, so its emptying rate is 1/40 of the tank per hour
Since tank B is twice the volume of tank A, the emptying rate of pipe R is twice the filling rates of pipes P and Q. Therefore, we can conclude that the effective emptying rate of pipe R is (1/10 + 1/12) - (1/40) = 11/120 of the tank per hour.
To find the time it takes to fill tank A, we need to calculate the net filling rate when all three pipes are operating simultaneously:
Net filling rate = Filling rate of pipes P and Q - Emptying rate of pipe R
= (1/10 + 1/12) - (11/120)
= 12/120 + 10/120 - 11/120
= 11/120
Therefore, the net filling rate is 11/120 of the tank per hour.
Now, let's calculate the time it takes to fill tank A:
Tank A = 1 unit
Net filling rate = 11/120 of the tank per hour
Time taken to fill tank A = 1 / (11/120) hours
= 120/11 hours
= 10 hours and 54 minutes
Since the options given are in hours and minutes, we can round up the time to the nearest hour and minute, which is 11 hours.
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Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. 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 Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. 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 Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A if R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?a)6 hrs 40 minutesb)8 hrs 30 minutesc)7 hrs 30 minutesd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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