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A rectangular reservoir is filled with water till one-fifth of the hei

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A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 18 Feb 2020, 05:12
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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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A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post Updated on: 18 Feb 2020, 08:09
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Bunuel 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
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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
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Originally posted by GMATPrepNow on 18 Feb 2020, 06:33.
Last edited by GMATPrepNow on 18 Feb 2020, 08:09, edited 1 time in total.
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A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post Updated on: 18 Feb 2020, 07:37
Reservoir: ( \(\frac{1}{5}\)) — filled with water
—> inlet tap can fill \(\frac{4}{5}\) of the reservoir in 2 hours ( \(\frac{2}{5}\) —in one hour, \(\frac{1}{5}\) — in 30 minutes)

—> \(\frac{4}{5} —\frac{1}{5} = (\frac{2}{5} —\frac{1}{5})*t\)

\(\frac{3}{5} = \frac{1}{5}*t\)
—> t = 3 hours

The answer is A

Posted from my mobile device

Originally posted by lacktutor on 18 Feb 2020, 07:30.
Last edited by lacktutor on 18 Feb 2020, 07:37, edited 1 time in total.
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Re: A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 18 Feb 2020, 07:36
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GMATPrepNow wrote:
Bunuel 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
Are You Up For the Challenge: 700 Level Questions


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)(4 gallons per hour) = 2 gallons.
So, after 30 minutes, the volume in the reservoir = 4 + 2 = 6 gallons.
So in order to FILL the reservoir to the top, we must add an additional 14 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 14 gallons of water, and we are doing so at a rate of 4 gallons per hour
Time = amount/rate
= (14 gallons)/(4 gallons per hour)
= 7/2 hours
= 3.5 hours

Answer: B

Cheers,
Brent


hi, Brent
I'm sorry if I made a mistake.
Can you check one more time the highlighted part above??
Shouldn't it be 4 gallons??
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Re: A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 18 Feb 2020, 08:11
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lacktutor wrote:
hi, Brent
I'm sorry if I made a mistake.
Can you check one more time the highlighted part above??
Shouldn't it be 4 gallons??


Ughh, silly mistake (it's like Bunuel predicted my error and made a corresponding answer choice specifically for me!)
Good catch!! I've edited my solution.
KUDOS FOR YOU!!

Cheers,
Brent
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Re: A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 18 Feb 2020, 09:23
GMATPrepNow wrote:
lacktutor wrote:
hi, Brent
I'm sorry if I made a mistake.
Can you check one more time the highlighted part above??
Shouldn't it be 4 gallons??


Ughh, silly mistake (it's like Bunuel predicted my error and made a corresponding answer choice specifically for me!)
Good catch!! I've edited my solution.
KUDOS FOR YOU!!

Cheers,
Brent


GMATPrepNow

Hi Brent,

Your solution is fantastic. But I have a query :-

In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?

Isn't it asking how much time it takes to fill the remaining 4/5th of the tank? i.e. Shouldn't we add initial 1/2 an hr that inlet pipe was opened alone to fill 1/5th of the remaining part and the 3 hrs that drainage pipe and inlet pipe take to fill the rest of the 3/5th of the tank? So the answer would be 3 and half hour in that case?
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Re: A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 18 Feb 2020, 10:20
Top Contributor
shameekv1989 wrote:
GMATPrepNow wrote:
lacktutor wrote:
hi, Brent
I'm sorry if I made a mistake.
Can you check one more time the highlighted part above??
Shouldn't it be 4 gallons??


Ughh, silly mistake (it's like Bunuel predicted my error and made a corresponding answer choice specifically for me!)
Good catch!! I've edited my solution.
KUDOS FOR YOU!!

Cheers,
Brent


GMATPrepNow

Hi Brent,

Your solution is fantastic. But I have a query :-

In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?

Isn't it asking how much time it takes to fill the remaining 4/5th of the tank? i.e. Shouldn't we add initial 1/2 an hr that inlet pipe was opened alone to fill 1/5th of the remaining part and the 3 hrs that drainage pipe and inlet pipe take to fill the rest of the 3/5th of the tank? So the answer would be 3 and half hour in that case?


Good question!
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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A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 21 Feb 2020, 23:29
The problem is, in an actual test, we are not allowed to make two choices so we have to analyze the language of the question and make the right call. In this context, this question is more of an exercise in reading comprehension than a mathematical problem since the actual calculation is fairly simple. So let's see what we have:

A reservoir with an inlet tap at the head and an outlet at the bottom is filled up to one-fifth of its capacity. I think that we can safely assume that both the inlet and outlet are closed at this point. From this point on, we are presented with three different scenarios each involving a certain course of action and the result thereof:
(a) The outlet is unplugged and consequently the reservoir is completely drained in 1 hour which gives us the information required to calculate the rate/efficiency of the outlet valve.
(b) The inlet tap is opened and the reservoir fills in 2 hours which gives us the information needed to calculate the efficiency of the inlet tap.
(c) This is the tricky part. The question stem asks: "In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?" In my opinion, the answer should be the TOTAL time (the 30 minutes when only the inlet tap is in play plus the time until the reservoir is full during which period both the inlet tap and the outlet valve are in play). There are two reasons why I have made this assumption:
(1) In all three scenarios, the actions start with the reservoir one-fifth full and both the inlet and outlet closed. So the time for the result of each action to culminate (draining in the first scenario and filling to the brim in the second and third scenarios) should be calculated from this starting point. In fact, in the given context the above question can be rephrased thus: " As in Scenario (b), the inlet tap is opened but this time the outlet valve is unplugged after 30 minutes. In this case, how much time will it take to fill up the reservoir?"
(2) Option B would have been the correct choice if the above question would have used the word "after" instead of "if": "In how much time will the the reservoir fill to the brim AFTER the outlet is unplugged 30 minutes from the time the inlet tap is opened?"

So, IMO, the answer is 3 hours 30 minutes (B)
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Re: A rectangular reservoir is filled with water till one-fifth of the hei  [#permalink]

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New post 23 Feb 2020, 09:59
let total reservoir be 10 ltrs
1/5 th filled = 2 ltrs
and outlet rate ; 2 ltr per hr
and intlet rate ; 10/2 ; 5 ltr per hr
net rate ; 5-2 ; 3 ltr per hr
for first 30 mins the reservoir would be filled ; 2*30/60 ; 1 ltr
now left with 9 ltrs would be filled in 9/3 ; 3 hrs
total time taken ; 3hrs and 30 mins
IMO B :)


Bunuel 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


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Re: A rectangular reservoir is filled with water till one-fifth of the hei   [#permalink] 23 Feb 2020, 09:59
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