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A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?
- a)36
- b)42
- c)48
- d)54
- e)60
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular tank has the dimensions of its base as 30 metres by 20 m...
Given:
- Length of rectangular tank = 30 meters
- Breadth of rectangular tank = 20 meters
- Height of rectangular tank = 10 meters
- Time taken by tap-1 to fill the entire tank = 60 hours
- Time taken by tap-2 to fill the entire tank = 90 hours
- Holes are at a height of 2 meters
- Height of first hole from the base = 2 meters
- Height of 2nd hole from the base = 4 meters
- Height of 3rd hole from the base = 6 meters
- Height of 4th hole from the base = 8 meters
- Rate of water outflow from each hole = 10m3 per hour
To Find: Time taken to fill the empty tank completely if both the taps are opened?
Approach:
- Work done = Rate * Time taken
- We know that work done is to fill the entire tank
- So, for finding the time taken, we need to find the rate of doing work.
- Rate of doing work = Rate of inflow by both the taps – Rate of outflow by the holes
- Rate of Inflow
- As we are given the time taken by both the taps individually to fill the tank, we can find the combined rate of ttaps to fill the tank.
- Combined rate of the taps = Rate of tap-I + Rate of tap-II
- As we are given the time taken by both the taps individually to fill the tank, we can find the combined rate of ttaps to fill the tank.
- Rate of Outflow
- However, the rate of outflow will not be constant throughout the tank, as it will depend on the number of holes from which the water is flowing out.
- For example, increasing the water level in tank from 2 meters to 4 meters will have a different rate than increasing the water level from 4 metres to 6 meters. This is because the number of holes from which the water is outflowing is different in both the cases.
- So, we will need to find the time taken separately to fill the tank between each of the holes
- However, the rate of outflow will not be constant throughout the tank, as it will depend on the number of holes from which the water is flowing out.
- Once we know the rate of inflow and the rate of outflow between each consecutive hole, we can find the net rate = Rate of inflow – Rate of outflow.
- Using the net rate, we can find the time taken to fill the tank between each consecutive hole.
- So, the total time taken to fill the tank = Sum of time taken to fill the tank between each consecutive hole.
Working out:
- Total work to do done = Total volume to be filled = Volume of tank = 30 *20 *10 = 6000 m3
- Rate of Inflow
3. Time Taken :
- As the holes are at an interval of 2 meters, we will calculate the time taken for 2 meters at a time.
- Hence the volume of water needed for increasing the height of the water by 2 meters in the tank 30 *20*2 m3
- We have subtracted 10 in the net rate because from 1 hole there would be outflow of water at a rate of 10 m3 per hour
- We have subtracted 10*2 in the net rate because from 2 holes there would be outflow of water each at a rate of 10 m3 per hour
- We have subtracted 10*3 in the net rate because from 3 holes there would be outflow of water each at a rate of 10 m3 per hour
- We have subtracted 10*4 in the net rate because from 4 holes there would be outflow of water each at a rate of 10 m3 per hour
4. Hence the total time taken would be ~ 7 +8+8+9+10 = 42 hours.
Answer B
Most Upvoted Answer
A rectangular tank has the dimensions of its base as 30 metres by 20 m...
Given data:
Dimensions of the tank: Length = 30m, Width = 20m, Height = 10m
Rate of filling the tank by tap 1 = 1/60 of the tank per hour
Rate of filling the tank by tap 2 = 1/90 of the tank per hour
Rate of water outflow from each hole = 10m per hour
Distance between holes = 2m
First hole is 2m above the base of the tank
To find: Time taken to fill the tank completely when both taps are opened simultaneously
Let's calculate the volume of the tank:
Volume = Length × Width × Height
Volume = 30m × 20m × 10m
Volume = 6000 cubic meters
Let's calculate the rate of water outflow from each hole:
Rate of water outflow from each hole = 10m per hour
Let's calculate the rate of water outflow from all the holes:
Number of holes = (Height - Distance of first hole from base) / Distance between holes + 1
Number of holes = (10m - 2m) / 2m + 1
Number of holes = 4 + 1
Number of holes = 5
Rate of water outflow from all the holes = Rate of water outflow from each hole × Number of holes
Rate of water outflow from all the holes = 10m per hour × 5
Rate of water outflow from all the holes = 50m per hour
Let's calculate the combined rate of filling the tank by both taps:
Combined rate of filling the tank = Rate of filling by tap 1 + Rate of filling by tap 2
Combined rate of filling the tank = 1/60 + 1/90
Combined rate of filling the tank = (3 + 2) / (3 × 60)
Combined rate of filling the tank = 5 / 180
Combined rate of filling the tank = 1/36 of the tank per hour
Now, let's calculate the time taken to fill the tank completely when both taps are opened simultaneously:
Time = Volume / Combined rate of filling the tank
Time = 6000 cubic meters / (1/36 of the tank per hour)
Time = 6000 cubic meters × 36 hours
Time = 216000 hours
Approximately, it will take 216000 hours to fill the tank completely when both taps are opened simultaneously.
Therefore, the correct answer is option (B) 42.
Dimensions of the tank: Length = 30m, Width = 20m, Height = 10m
Rate of filling the tank by tap 1 = 1/60 of the tank per hour
Rate of filling the tank by tap 2 = 1/90 of the tank per hour
Rate of water outflow from each hole = 10m per hour
Distance between holes = 2m
First hole is 2m above the base of the tank
To find: Time taken to fill the tank completely when both taps are opened simultaneously
Let's calculate the volume of the tank:
Volume = Length × Width × Height
Volume = 30m × 20m × 10m
Volume = 6000 cubic meters
Let's calculate the rate of water outflow from each hole:
Rate of water outflow from each hole = 10m per hour
Let's calculate the rate of water outflow from all the holes:
Number of holes = (Height - Distance of first hole from base) / Distance between holes + 1
Number of holes = (10m - 2m) / 2m + 1
Number of holes = 4 + 1
Number of holes = 5
Rate of water outflow from all the holes = Rate of water outflow from each hole × Number of holes
Rate of water outflow from all the holes = 10m per hour × 5
Rate of water outflow from all the holes = 50m per hour
Let's calculate the combined rate of filling the tank by both taps:
Combined rate of filling the tank = Rate of filling by tap 1 + Rate of filling by tap 2
Combined rate of filling the tank = 1/60 + 1/90
Combined rate of filling the tank = (3 + 2) / (3 × 60)
Combined rate of filling the tank = 5 / 180
Combined rate of filling the tank = 1/36 of the tank per hour
Now, let's calculate the time taken to fill the tank completely when both taps are opened simultaneously:
Time = Volume / Combined rate of filling the tank
Time = 6000 cubic meters / (1/36 of the tank per hour)
Time = 6000 cubic meters × 36 hours
Time = 216000 hours
Approximately, it will take 216000 hours to fill the tank completely when both taps are opened simultaneously.
Therefore, the correct answer is option (B) 42.
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A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer?
Question Description
A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer?.
A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer?.
Solutions for A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
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A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A rectangular tank has the dimensions of its base as 30 metres by 20 metres and a height of 10 metres. There are two taps attached to the tank such that each tap working alone at a constant rate can fill the tank completely in 60 hours and 90 hours respectively. One of the walls of the tank has holes along the height of the tank at a regular distance of 2 metres and the first such hole is 2 metres above the base of the tank. The rate of water outflow from each hole is 10m per hour. If both the taps are opened simultaneously in the empty tank, approximately how many hours will it take to fill the tank completely?a)36b)42c)48d)54e)60Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice UPSC tests.
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