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A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?
- a)209
- b)211
- c)213
- d)215
- e)217
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A and B are only inlets and C is an outlet of a circular water tank. A...
Solution: Let volume of the tank be 600x litres.
Inlets A and B will fill 20x and 15x litres of water in the tank in one minute. Outlet C will let go 12x litres of water in a minute.
After a cycle of 4 minutes the tank will have (20 - 12 + 15 - 12)x = 11x litres of water.
At the end of 54 ‘4 minute cycles’, tank will have 54 x 11x = 594x litres.
Now, at the 53rd cycle the tank will have 583x litres of water. 20x litres of water will be added in the next minute.
Inlets A and B will fill 20x and 15x litres of water in the tank in one minute. Outlet C will let go 12x litres of water in a minute.
After a cycle of 4 minutes the tank will have (20 - 12 + 15 - 12)x = 11x litres of water.
At the end of 54 ‘4 minute cycles’, tank will have 54 x 11x = 594x litres.
Now, at the 53rd cycle the tank will have 583x litres of water. 20x litres of water will be added in the next minute.
In the (53 x 4) + 1 = 213rd minute the tank will overflow.
Thus, after 213 minutes the cycle should be stopped. Hence, option 3.
Thus, after 213 minutes the cycle should be stopped. Hence, option 3.
Most Upvoted Answer
A and B are only inlets and C is an outlet of a circular water tank. A...
To solve this problem, let's break it down step by step:
Step 1: Determine the rates of filling and emptying
Inlet A takes 30 minutes to fill the tank, so its filling rate is 1/30 of the tank per minute.
Inlet B takes 40 minutes to fill the tank, so its filling rate is 1/40 of the tank per minute.
Outlet C takes 50 minutes to empty the tank, so its emptying rate is 1/50 of the tank per minute.
Step 2: Calculate the net filling or emptying rate
Since the tank is being filled and emptied alternately, we need to calculate the net rate of filling or emptying after each cycle.
During the first cycle:
Inlet A is open for 1 minute, so it fills 1/30 of the tank.
Outlet C is open for 1 minute, so it empties 1/50 of the tank.
Therefore, the net filling or emptying rate after the first cycle is:
1/30 - 1/50 = 5/150 - 3/150 = 2/150 = 1/75 of the tank per minute.
During the second cycle:
Inlet B is open for 1 minute, so it fills 1/40 of the tank.
Outlet C is open for 1 minute, so it empties 1/50 of the tank.
Therefore, the net filling or emptying rate after the second cycle is:
1/40 - 1/50 = 5/200 - 4/200 = 1/200 of the tank per minute.
Step 3: Determine the number of cycles needed to fill the tank
Since the net filling or emptying rate decreases after each cycle, we need to calculate how many cycles it takes to reach a net filling rate of 0, indicating that the tank is full.
Let's assume it takes n cycles to fill the tank completely. At the end of the nth cycle, the net filling or emptying rate is 0.
The total amount filled during the nth cycle is:
n/75 - n/200 = 0
Simplifying this equation, we get:
n/75 = n/200
Cross-multiplying, we get:
200n = 75n
Dividing both sides by n, we get:
200 = 75
This is not possible, so our assumption is incorrect. Therefore, it must take more than n cycles to fill the tank completely.
Step 4: Calculate the total time to fill the tank
Since the net filling or emptying rate decreases after each cycle, we can calculate the total time to fill the tank by summing the times for each cycle.
The total time to fill the tank is given by the formula:
Total time = (1/30 + 1/50) + (1/40 + 1/50) + ... + (1/75 + 1/200)
Simplifying this expression, we get:
Total time = (5/150 + 5/200) + (4/200 + 4/250) + ... + (1/75 + 1/200)
Total time = 5(1/30 - 1/50) + 4(1/40 - 1/50) + ... + 1/75
Total time = 5(2/
Step 1: Determine the rates of filling and emptying
Inlet A takes 30 minutes to fill the tank, so its filling rate is 1/30 of the tank per minute.
Inlet B takes 40 minutes to fill the tank, so its filling rate is 1/40 of the tank per minute.
Outlet C takes 50 minutes to empty the tank, so its emptying rate is 1/50 of the tank per minute.
Step 2: Calculate the net filling or emptying rate
Since the tank is being filled and emptied alternately, we need to calculate the net rate of filling or emptying after each cycle.
During the first cycle:
Inlet A is open for 1 minute, so it fills 1/30 of the tank.
Outlet C is open for 1 minute, so it empties 1/50 of the tank.
Therefore, the net filling or emptying rate after the first cycle is:
1/30 - 1/50 = 5/150 - 3/150 = 2/150 = 1/75 of the tank per minute.
During the second cycle:
Inlet B is open for 1 minute, so it fills 1/40 of the tank.
Outlet C is open for 1 minute, so it empties 1/50 of the tank.
Therefore, the net filling or emptying rate after the second cycle is:
1/40 - 1/50 = 5/200 - 4/200 = 1/200 of the tank per minute.
Step 3: Determine the number of cycles needed to fill the tank
Since the net filling or emptying rate decreases after each cycle, we need to calculate how many cycles it takes to reach a net filling rate of 0, indicating that the tank is full.
Let's assume it takes n cycles to fill the tank completely. At the end of the nth cycle, the net filling or emptying rate is 0.
The total amount filled during the nth cycle is:
n/75 - n/200 = 0
Simplifying this equation, we get:
n/75 = n/200
Cross-multiplying, we get:
200n = 75n
Dividing both sides by n, we get:
200 = 75
This is not possible, so our assumption is incorrect. Therefore, it must take more than n cycles to fill the tank completely.
Step 4: Calculate the total time to fill the tank
Since the net filling or emptying rate decreases after each cycle, we can calculate the total time to fill the tank by summing the times for each cycle.
The total time to fill the tank is given by the formula:
Total time = (1/30 + 1/50) + (1/40 + 1/50) + ... + (1/75 + 1/200)
Simplifying this expression, we get:
Total time = (5/150 + 5/200) + (4/200 + 4/250) + ... + (1/75 + 1/200)
Total time = 5(1/30 - 1/50) + 4(1/40 - 1/50) + ... + 1/75
Total time = 5(2/
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A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer?
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A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct 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 A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct 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 A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer?.
A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct 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 A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct 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 A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer?.
Solutions for A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A and B are only inlets and C is an outlet of a circular water tank. A and B take 30 and 40 minutes respectively to fill the whole tank independently. Outlet C takes 50 minutes to empty the completely filled tank. Initially the tank is empty and inlet A is put on for a minute then it is closed and outlet C is put on for one minute; then it is closed. Now, inlet B is opened for one minute and then closed followed by putting on outlet C for 1 minute. Once the tank is full, the cycle is stopped at the end of the minute. After how many minutes the cycle should be stopped?a)209b)211c)213d)215e)217Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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