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A rectangular reservoir is filled with water till one-fifth

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A rectangular reservoir is filled with water till one-fifth [#permalink] New post   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
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   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



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
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A rectangular reservoir is filled with water till one-fifth [#permalink] New post   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


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
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   15 Apr 2020, 21:30
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GreenlightTestPrep wrote:
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


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

Answer: A

Cheers,
Brent




It can not be A
i used two approaches and answer is B.
Approach 1
let the capacity of the tank=50
so it is filled now 10
40 will be filled in 2 hours ,=20 will be filled in 1 hour= rate of inlet
50 will be drained in 1 hour=rate of outlet
now inlet is opened 30 minutes earlier= worked 1/2 earlier than outlet=1/2*20=10 is filled in 30 minutes.

after this they will work together(more like a car chase run concept and inlet have to overcome outlet to fill the tank)
here is shortcut

reaming work for inlet=40
for outlet=50
so apply work1+work2/rate outlet-rate inlet
we get the time in which tank will be filled if they both are operational
40+50/50-20
90/30=3 hours
now to get the time taken by the inlet to fill the tank we have to add the 30 minutes also
so time taken by inlet is 3 hours and 30 minutes.
it cant be A
Ans
B
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   15 Apr 2020, 21:48
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GreenlightTestPrep wrote:
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


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

Answer: A

Cheers,
Brent



Approach 2, by using your explanation.
they are working in opposite direction so i can apply shortcut based on two objects moving towards each other.
so work done by inlet in 30 minutes is 4. remaining is 16
outlet have to work 20
together they both will work 20+16=36
so 36/rate1+rate2
36/8+4
36/12=3 hours

now it is the time they work together, now inlet has taken as whole 3 +30 minutes.
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   16 Apr 2020, 05:52
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suhaibwahla wrote:
It can not be A
i used two approaches and answer is B.
Approach 1
let the capacity of the tank=50
so it is filled now 10
40 will be filled in 2 hours ,=20 will be filled in 1 hour= rate of inlet
50 will be drained in 1 hour=rate of outlet
now inlet is opened 30 minutes earlier= worked 1/2 earlier than outlet=1/2*20=10 is filled in 30 minutes.

after this they will work together(more like a car chase run concept and inlet have to overcome outlet to fill the tank)
here is shortcut

reaming work for inlet=40
for outlet=50
so apply work1+work2/rate outlet-rate inlet
we get the time in which tank will be filled if they both are operational
40+50/50-20
90/30=3 hours
now to get the time taken by the inlet to fill the tank we have to add the 30 minutes also
so time taken by inlet is 3 hours and 30 minutes.
it cant be A
Ans
B


Great observation!
The question is a little bit ambiguous: " In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?"
So, are we starting the clock AFTER we unplug the outlet valve, or when we first open the INLET TAP?

If we start the clock when we unplug the outlet valve, then the answer is 3 hours
If we start the clock when we first open the INLET TAP, then the answer is 3.5 hours

Cheers,
Brent
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   24 Jun 2022, 00:56
RSQUANT wrote:
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



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


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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   05 Sep 2022, 15:20
GreenlightTestPrep wrote:
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


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

Answer: A

Cheers,
Brent



I agree with your method overall. However, at the end, you forgot the final step to add your initial 30 minutes (from when the bottom was plugged for 30 minutes and you went from 4 gallons to 8 gallons). If you add this 30 minutes back, you will get 3 hours and 30 minutes = B.
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Re: A rectangular reservoir is filled with water till one-fifth [#permalink] New post   10 Dec 2023, 12:46
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If outlet pipe drains tank in 1 hour Rate = 1/5

Inlet pipe fills tank in 2hours so rate will be fraction of volume left 4/5 which fills up in 2 hours

R = 4/5/2

2/5




Inlet pipe operates for 30 minutes, fraction of water added to tank x


2/5= x/1/2

x= 1/5


Fraction of water now in tank

1/5 + 1/5 = 2/5

Fraction of volume left to be filled 1 - 2/5

= 3/5


Now both pipes become operational. Time required for tank to be filled t

2/5 - 1/5 = 3/5/t

1/5 = 3/5t

5t = 15

t = 3

Add initial thirty minutes to give 3 hours 30 minutes Answer B

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