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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
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A and B are only inlets and C is an outlet of a circular water tank. ...
To solve this problem, we need to understand the rates at which the inlets and outlet fill or empty the tank. Let's break down the problem step by step to find the answer.
Step 1: Find the rates of the inlets and outlet
- Inlet A fills the tank in 30 minutes, so its filling rate is 1/30 of the tank per minute.
- Inlet B fills the tank in 40 minutes, so its filling rate is 1/40 of the tank per minute.
- Outlet C empties the tank in 50 minutes, so its emptying rate is 1/50 of the tank per minute.
Step 2: Calculate the net rate of filling or emptying
When both inlets A and B are open, their combined filling rate is (1/30 + 1/40) = 7/120 of the tank per minute.
When outlet C is open, it empties the tank at a rate of 1/50 of the tank per minute.
Step 3: Determine the time it takes to fill the tank
To find the time it takes to fill the tank, we need to calculate the reciprocal of the net filling rate.
Net filling rate = 7/120 - 1/50 = (35 - 24)/600 = 11/600 of the tank per minute.
Time taken to fill the tank = reciprocal of the net filling rate = 600/11 minutes.
Step 4: Calculate the number of cycles completed before the tank is full
In each cycle, the tank is filled for a minute and emptied for a minute. Therefore, each cycle takes 2 minutes.
The number of cycles completed before the tank is full = time taken to fill the tank divided by the duration of each cycle.
Number of cycles = (600/11) / 2 = 300/11.
Step 5: Find the time when the cycle should be stopped
To find the time when the cycle should be stopped, we need to calculate the duration of the completed cycles and the remaining time.
Duration of completed cycles = number of cycles * duration of each cycle = (300/11) * 2 = 600/11 minutes.
Remaining time = time taken to fill the tank - duration of completed cycles = (600/11) - (600/11) = 0 minutes.
Since the remaining time is 0 minutes, the cycle should be stopped at the end of the minute. Therefore, the cycle should be stopped after 213 minutes, which is the duration of the completed cycles.
Hence, the correct answer is option C) 213.
Step 1: Find the rates of the inlets and outlet
- Inlet A fills the tank in 30 minutes, so its filling rate is 1/30 of the tank per minute.
- Inlet B fills the tank in 40 minutes, so its filling rate is 1/40 of the tank per minute.
- Outlet C empties the tank in 50 minutes, so its emptying rate is 1/50 of the tank per minute.
Step 2: Calculate the net rate of filling or emptying
When both inlets A and B are open, their combined filling rate is (1/30 + 1/40) = 7/120 of the tank per minute.
When outlet C is open, it empties the tank at a rate of 1/50 of the tank per minute.
Step 3: Determine the time it takes to fill the tank
To find the time it takes to fill the tank, we need to calculate the reciprocal of the net filling rate.
Net filling rate = 7/120 - 1/50 = (35 - 24)/600 = 11/600 of the tank per minute.
Time taken to fill the tank = reciprocal of the net filling rate = 600/11 minutes.
Step 4: Calculate the number of cycles completed before the tank is full
In each cycle, the tank is filled for a minute and emptied for a minute. Therefore, each cycle takes 2 minutes.
The number of cycles completed before the tank is full = time taken to fill the tank divided by the duration of each cycle.
Number of cycles = (600/11) / 2 = 300/11.
Step 5: Find the time when the cycle should be stopped
To find the time when the cycle should be stopped, we need to calculate the duration of the completed cycles and the remaining time.
Duration of completed cycles = number of cycles * duration of each cycle = (300/11) * 2 = 600/11 minutes.
Remaining time = time taken to fill the tank - duration of completed cycles = (600/11) - (600/11) = 0 minutes.
Since the remaining time is 0 minutes, the cycle should be stopped at the end of the minute. Therefore, the cycle should be stopped after 213 minutes, which is the duration of the completed cycles.
Hence, the correct answer is option C) 213.
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Community Answer
A and B are only inlets and C is an outlet of a circular water tank. ...
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.
In the (53 x 4) + 1 = 213rd minute the tank will overflow.
Thus, after 213 minutes the cycle should be stopped. Hence, option 3.
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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)215Correct 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)215Correct 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)215Correct 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)215Correct 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)215Correct 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)215Correct 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)215Correct 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)215Correct 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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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)215Correct 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)215Correct 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)215Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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