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Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?
- a)216
- b)108
- c)112
- d)224
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two pipes individually can fill a tank in 14 hours and 16 hours, respe...
Let the capacity of the tank = LCM of 14 and 16 = 112 L
So, the rates of filling of the two pipes = 112/14 = 8 L/hr and 112/16 = 7 L/hr
So, effective filling rate = 8 + 7 = 15 L/hr
Ideally, time taken to fill the tank
Actual time taken = 32 minutes + 7 hours 28 minutes = 8 hours
Thus, actual filling rate = 112/8 = 14 L/hr
So, the rates of filling of the two pipes = 112/14 = 8 L/hr and 112/16 = 7 L/hr
So, effective filling rate = 8 + 7 = 15 L/hr
Ideally, time taken to fill the tank
Actual time taken = 32 minutes + 7 hours 28 minutes = 8 hours
Thus, actual filling rate = 112/8 = 14 L/hr
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Community Answer
Two pipes individually can fill a tank in 14 hours and 16 hours, respe...
Let's assume that the tank has a capacity of 1 unit.
To find the rates at which each pipe fills the tank, we can calculate the fraction of the tank filled by each pipe in one hour.
Pipe 1 fills the tank in 14 hours, so in one hour it fills 1/14th of the tank.
Pipe 2 fills the tank in 16 hours, so in one hour it fills 1/16th of the tank.
When both pipes are opened simultaneously, the combined rate at which they fill the tank is the sum of their individual rates.
So, the combined rate is (1/14 + 1/16) = (8 + 7)/112 = 15/112 of the tank per hour.
Now, let's consider the scenario where the outlet pipe at the bottom of the tank is also opened.
Due to the outlet pipe being opened, the effective filling rate of the tank decreases.
To find the new effective filling rate, we need to consider the extra time it takes to fill the tank.
We are given that it takes an extra 32 minutes to fill the tank.
In 32 minutes, the combined filling rate of the two pipes is (15/112) * (32/60) = 4/112 = 1/28 of the tank.
So, the effective filling rate of the two pipes, considering the outlet pipe, is 1/28 less than their combined rate.
Therefore, the effective filling rate is (15/112) - (1/28) = 13/112 of the tank per hour.
To find the time taken to fill a tank double the size, we can use the effective filling rate.
If the tank is double the size, it has a capacity of 2 units.
The time taken to fill a tank double the size is (2 units) / (13/112 units per hour) = (2 * 112) / 13 = 224/13 hours.
So, the outlet pipe will take 224/13 hours to completely empty a tank double the size.
Therefore, the correct answer is option D) 224.
To find the rates at which each pipe fills the tank, we can calculate the fraction of the tank filled by each pipe in one hour.
Pipe 1 fills the tank in 14 hours, so in one hour it fills 1/14th of the tank.
Pipe 2 fills the tank in 16 hours, so in one hour it fills 1/16th of the tank.
When both pipes are opened simultaneously, the combined rate at which they fill the tank is the sum of their individual rates.
So, the combined rate is (1/14 + 1/16) = (8 + 7)/112 = 15/112 of the tank per hour.
Now, let's consider the scenario where the outlet pipe at the bottom of the tank is also opened.
Due to the outlet pipe being opened, the effective filling rate of the tank decreases.
To find the new effective filling rate, we need to consider the extra time it takes to fill the tank.
We are given that it takes an extra 32 minutes to fill the tank.
In 32 minutes, the combined filling rate of the two pipes is (15/112) * (32/60) = 4/112 = 1/28 of the tank.
So, the effective filling rate of the two pipes, considering the outlet pipe, is 1/28 less than their combined rate.
Therefore, the effective filling rate is (15/112) - (1/28) = 13/112 of the tank per hour.
To find the time taken to fill a tank double the size, we can use the effective filling rate.
If the tank is double the size, it has a capacity of 2 units.
The time taken to fill a tank double the size is (2 units) / (13/112 units per hour) = (2 * 112) / 13 = 224/13 hours.
So, the outlet pipe will take 224/13 hours to completely empty a tank double the size.
Therefore, the correct answer is option D) 224.
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Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer?
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Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer?.
Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer?.
Solutions for Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Two pipes individually can fill a tank in 14 hours and 16 hours, respectively. The pipes are opened simultaneously, but by mistake, the outlet pipe at the bottom of the tank was opened as well. Due to this, it took 32 extra minutes for the tank to be filled up. Considering that the tank is full, how much time (in hours) will the outlet pipe take to completely empty a tank double the size?a)216b)108c)112d)224Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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