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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?
- a)72 hours
- b)62 hours
- c)64 hours
- d)84 hours
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 12 hours and 18 hours respectivel...
Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108).
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.
Most Upvoted Answer
Two pipes A and B can fill a tank in 12 hours and 18 hours respectivel...
Given information:
- Pipe A can fill the tank in 12 hours.
- Pipe B can fill the tank in 18 hours.
- Due to a leakage, it took an additional 48 minutes to fill the tank.
Let's calculate the filling rates of pipes A and B:
- Pipe A fills 1/12th of the tank in 1 hour.
- Pipe B fills 1/18th of the tank in 1 hour.
Let's assume the capacity of the tank is T and the rate of leakage is L (in liters per hour).
Filling the tank without leakage:
- Pipe A fills the tank in T/12 hours.
- Pipe B fills the tank in T/18 hours.
Filling the tank with leakage:
- Pipe A fills the tank in (T/12 + 48/60) hours (converted 48 minutes to hours).
- Pipe B fills the tank in (T/18 + 48/60) hours.
Since both pipes are opened simultaneously, their combined filling rate is the sum of their individual rates:
- Pipe A and B together fill 1/12 + 1/18 = 5/36th of the tank in 1 hour.
Finding the time taken to fill the tank with leakage:
- Pipe A and B together fill the tank in (T/12 + 48/60) hours.
- In 1 hour, they fill 5/36th of the tank.
- So, (T/12 + 48/60) * (5/36) = T
Simplifying the equation:
- (T/12 + 48/60) * (5/36) = T
- (5T + 4T) / (12*5) = T
- (9T/60) = T
- 9T = 60T
- 9T - 60T = 0
- -51T = 0
- T = 0
Since the time taken to fill the tank with leakage is 0, it means the leak is emptying the tank faster than the combined filling rate of pipes A and B.
Therefore, the leak will empty the tank in a certain amount of time. The correct answer option is A) 72 hours.
- Pipe A can fill the tank in 12 hours.
- Pipe B can fill the tank in 18 hours.
- Due to a leakage, it took an additional 48 minutes to fill the tank.
Let's calculate the filling rates of pipes A and B:
- Pipe A fills 1/12th of the tank in 1 hour.
- Pipe B fills 1/18th of the tank in 1 hour.
Let's assume the capacity of the tank is T and the rate of leakage is L (in liters per hour).
Filling the tank without leakage:
- Pipe A fills the tank in T/12 hours.
- Pipe B fills the tank in T/18 hours.
Filling the tank with leakage:
- Pipe A fills the tank in (T/12 + 48/60) hours (converted 48 minutes to hours).
- Pipe B fills the tank in (T/18 + 48/60) hours.
Since both pipes are opened simultaneously, their combined filling rate is the sum of their individual rates:
- Pipe A and B together fill 1/12 + 1/18 = 5/36th of the tank in 1 hour.
Finding the time taken to fill the tank with leakage:
- Pipe A and B together fill the tank in (T/12 + 48/60) hours.
- In 1 hour, they fill 5/36th of the tank.
- So, (T/12 + 48/60) * (5/36) = T
Simplifying the equation:
- (T/12 + 48/60) * (5/36) = T
- (5T + 4T) / (12*5) = T
- (9T/60) = T
- 9T = 60T
- 9T - 60T = 0
- -51T = 0
- T = 0
Since the time taken to fill the tank with leakage is 0, it means the leak is emptying the tank faster than the combined filling rate of pipes A and B.
Therefore, the leak will empty the tank in a certain amount of time. The correct answer option is A) 72 hours.
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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer?
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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer?.
Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?a)72 hoursb)62 hoursc)64 hoursd)84 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer?.
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