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A rectangular reservoir is filled with water till one-fifth
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15 Apr 2020, 08:39
15 Apr 2020, 08:39
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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
(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
Re: A rectangular reservoir is filled with water till one-fifth
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25 Apr 2020, 06:59
25 Apr 2020, 06:59
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Carcass wrote:
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
(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
Outlet can drain the water in 1 hour i.e. 1/5th of reservoir in 1 hr
The inlet can fill 4/5th of the tank in 2 hrs
So when both of them work together the outlet will empty 1/5th of the reservoir while the inlet will fill 2/5th of the reservoir in one hour . Effectively they will fill 1/5th in one hour
So when inlet is opened for 30 mins i.e. 1/2 hr it will fill 1/5th of the tank .
So the tank is 2/5th filled and now both of them are going to work
They have to fill 3/5th which will take 3 hrs as they fill 1/5th of the tank each hour. So total 3 1/2 hrs
General Discussion
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A rectangular reservoir is filled with water till one-fifth
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15 Apr 2020, 09:21
15 Apr 2020, 09:21
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Carcass wrote:
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
(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
To make things easier on ourselves, let's assign a "nice" value to the total volume of the reservoir.
Let's say the reservoir holds a TOTAL of 20 gallons
A rectangular reservoir is filled with water till one-fifth of the height of the reservoir.
1/5 of 20 = 4
So, the reservoir currently holds 4 gallons of water
If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour.
In other words, 4 gallons of water will drain out of the reservoir in one hour.
Rate = amount/time = (4 gallons)/(1 hour) = 4 gallons per hour
So the RATE at which water drains out of the outlet = 4 gallons per 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 other words, it will take 2 hours for the inlet tap to add the additional 16 gallons of water it will take to fill the reservoir.
Rate = amount/time = (16 gallons)/(2 hours) = 8 gallons per hour
So the RATE at which water flows into the reservoir = 8 gallons per hour
In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?
If the inlet tap is opened for 30 minutes (aka 0.5 HOURS), the amount of water flowing into the reservoir = (0.5 hours)(8 gallons per hour) = 4 gallons.
So, after 30 minutes, the volume in the reservoir = 4 + 4 = 8 gallons.
So in order to FILL the reservoir to the top, we must add an additional 12 gallons of water
Once the outlet is unplugged, we have water flowing IN at a rate of 8 gallons per hour, and we have water flowing OUT at a rate of 4 gallons per hour
So the NET EFFECT = 8 gallons per hour - 4 gallons per hour = 4 gallons per hour
We need to add an additional 12 gallons of water, and we are doing so at a rate of 4 gallons per hour
Time = amount/rate
= (12 gallons)/(4 gallons per hour)
= 3 hours
IMPORTANT: Now we must add the 30 minutes that elapsed before the outlet was unplugged.
We get 3 hours + 30 minutes
Answer: B
