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A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?
- a)3 hours
- b)3 hours 30 minutes
- c)4 hours 30 minutes
- d)5 hours
- e)The reservoir will never be filled to the brim
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular reservoir is filled with water till one-fifth of the hei...
Given:
- Let the length and the breadth (of the base) of the reservoir be L and B, and let its height be H
- Time taken to drain the water in the reservoir is 1 hour
- Time taken to fill the reservoir completely (when V/5 water is already there) is 2 hours
To Find: Time taken to fill the reservoir if outlet is unplugged 30 minutes after inlet is opened
Approach:
- Here, 30 minutes is the time for which only the inlet pipe is opened
- (Volume that remains to be filled after 30 minutes of inlet) = (Volume that initially needed to be filled) – (Volume of water pumped in through the inlet in 30 minutes)
- And, Net Rate of Filling = Rate of Filling – Rate of Draining
Working out:
- Finding the Volume that Remains to be filled after 30 minutes of inlet
- (Volume that remains to be filled after 30 minutes of inlet) = (Volume that initially needed to be filled) – (Volume of water pumped in through the inlet in 30 minutes)
Looking at the answer choices, we see that the correct answer is Option B
Most Upvoted Answer
A rectangular reservoir is filled with water till one-fifth of the hei...
Given:
- The information given in the question can be visualized as under:
- Let the length and the breadth (of the base) of the reservoir be L and B, and let its height be H
- So, volume of reservoir = LBH = V(say)
- And, Volume of water in the reservoir = LBH / 5 = V / 5
- Time taken to drain the water in the reservoir is 1 hour
- S, rate of draining =
Volume to be drained / Time for draining = V / 5 volume units per hour
- Time taken to fill the reservoir completely (when V/5 water is already there) is 2 hours
- So, rate of filling =
Volume to be filled / Time for filling = 4V / 5 / 2 = 2V / 5 volume units per hour
To Find: Time taken to fill the reservoir if outlet is unplugged 30 minutes after inlet is opened
Approach:
1. Time taken(to go from V / 5 volume of water to V volume of water in the reservoir) = 30 minutes +
Volume that remains to be filled after 30minutes of inlet / Nat Rate of filling
1. Time taken(to go from V / 5 volume of water to V volume of water in the reservoir) = 30 minutes +
Volume that remains to be filled after 30minutes of inlet / Nat Rate of filling
- Here, 30 minutes is the time for which only the inlet pipe is opened
- (Volume that remains to be filled after 30 minutes of inlet) = (Volume that initially needed to be filled) – (Volume of water pumped in through the inlet in 30 minutes)
- And, Net Rate of Filling = Rate of Filling – Rate of Draining
Working out:
- Finding the Volume that Remains to be filled after 30 minutes of inlet
- (Volume that remains to be filled after 30 minutes of inlet) = (Volume that initially needed to be filled) – (Volume of water pumped in through the inlet in 30 minutes)
- = 4V / 5 – (Rate of filling) * (30 / 60 hour)
- = 4V / 5 – (2V / 5) (1 / 2)
- = 4V / 5 – V / 5
- = 3V / 5 volume units
- Finding the Net Rate of filling
- Rate of filling = 2V / 5 volume units per hour
- Rate of Draining = V / 5 volume units per hour
So, Net Rate of filling =
2V / 5 – V / 5 volume units per hour = V / 5 volume units per ho
2V / 5 – V / 5 volume units per hour = V / 5 volume units per ho
- Finding the Time Taken
Total time taken = 30 minutes + 3V / 5 / V / 5 hours
= 30 minutes + 3 hours
That is, 3 hours 30 minutes
= 30 minutes + 3 hours
That is, 3 hours 30 minutes
Looking at the answer choices, we see that the correct answer is Option B
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Community Answer
A rectangular reservoir is filled with water till one-fifth of the hei...
Understanding the Problem
The reservoir is initially filled to one-fifth of its height. We need to analyze the effects of both the outlet and the inlet on the water level.
Given Data
- The reservoir drains completely in 1 hour when the outlet is unplugged.
- The inlet fills the reservoir to the brim in 2 hours when the outlet is plugged.
Calculating Rates
- Drainage Rate: Since the outlet drains the reservoir in 1 hour, the rate of drainage is 1/5 of the reservoir per hour.
- Filling Rate: The inlet fills the reservoir in 2 hours, meaning the filling rate is 1/5 of the reservoir per hour.
Scenario Analysis
- First 30 Minutes with Inlet Open:
- In 0.5 hours, the inlet will fill 0.5 * (1/5) = 1/10 of the reservoir.
- After 30 minutes, the reservoir will have 1/5 + 1/10 = 3/10 of its height.
- Next 30 Minutes with Inlet Open and Outlet Unplugged:
- The outlet will drain 1/5 of the reservoir in the next hour.
- In the same hour, the inlet fills another 1/5 of the reservoir.
- The net effect is 1/5 (filled) - 1/5 (drained) = reservoir level remains at 3/10.
Final Filling Calculation
- Remaining Volume to Fill: The reservoir needs to reach full capacity from 3/10 to 1 (i.e., 7/10 of the reservoir).
- Net Rate After 1 Hour: After the first hour, the filling rate is still 1/5 per hour (since the outflow and inflow are equal).
- Time Required to Fill Remaining Volume:
- To fill 7/10 at a rate of 1/5, it will take (7/10) / (1/5) = 7/2 = 3.5 hours.
Conclusion
- Total Time:
- First 1 hour (30 mins with only inlet, 30 mins with both inlet and outlet) + 3.5 hours = 4.5 hours or 4 hours and 30 minutes.
Thus, the correct answer is option B (3 hours 30 minutes).
The reservoir is initially filled to one-fifth of its height. We need to analyze the effects of both the outlet and the inlet on the water level.
Given Data
- The reservoir drains completely in 1 hour when the outlet is unplugged.
- The inlet fills the reservoir to the brim in 2 hours when the outlet is plugged.
Calculating Rates
- Drainage Rate: Since the outlet drains the reservoir in 1 hour, the rate of drainage is 1/5 of the reservoir per hour.
- Filling Rate: The inlet fills the reservoir in 2 hours, meaning the filling rate is 1/5 of the reservoir per hour.
Scenario Analysis
- First 30 Minutes with Inlet Open:
- In 0.5 hours, the inlet will fill 0.5 * (1/5) = 1/10 of the reservoir.
- After 30 minutes, the reservoir will have 1/5 + 1/10 = 3/10 of its height.
- Next 30 Minutes with Inlet Open and Outlet Unplugged:
- The outlet will drain 1/5 of the reservoir in the next hour.
- In the same hour, the inlet fills another 1/5 of the reservoir.
- The net effect is 1/5 (filled) - 1/5 (drained) = reservoir level remains at 3/10.
Final Filling Calculation
- Remaining Volume to Fill: The reservoir needs to reach full capacity from 3/10 to 1 (i.e., 7/10 of the reservoir).
- Net Rate After 1 Hour: After the first hour, the filling rate is still 1/5 per hour (since the outflow and inflow are equal).
- Time Required to Fill Remaining Volume:
- To fill 7/10 at a rate of 1/5, it will take (7/10) / (1/5) = 7/2 = 3.5 hours.
Conclusion
- Total Time:
- First 1 hour (30 mins with only inlet, 30 mins with both inlet and outlet) + 3.5 hours = 4.5 hours or 4 hours and 30 minutes.
Thus, the correct answer is option B (3 hours 30 minutes).
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A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer?
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A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect 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 reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect 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 reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer?.
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A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened?a)3 hoursb)3 hours 30 minutesc)4 hours 30 minutesd)5 hourse)The reservoir will never be filled to the brimCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice UPSC tests.
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