It is currently 12 Dec 2017, 17:50

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

There are two inlets and one outlet to a cistern. One of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Manager
Manager
User avatar
B
Joined: 14 Jan 2013
Posts: 151

Kudos [?]: 386 [2], given: 30

Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 09 Mar 2014, 01:40
2
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:00) correct 31% (01:51) wrong based on 250 sessions

HideShow timer Statistics

There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?

(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours
[Reveal] Spoiler: OA

_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Kudos [?]: 386 [2], given: 30

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135394 [1], given: 12691

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 09 Mar 2014, 02:19
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
Mountain14 wrote:
There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?

(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours


The combined inflow rate of the two inlets is 1/3 + 1/6 = 1/2 cistern/hour. Thus, working together, it takes 2 hours (time is reciprocal of rate) to fill the cistern.

From 9:00 AM to 10:30 AM, so in 1.5=3/2 hours, the inlet pipes will fill (time)*(rate) = 3/2*1/2 = 3/4 th of the cistern .

Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.

Letting x to be the rate of the outlet, we would have: 1/2 - x = 1/4 --> x = 1/4 cistern/hour, which means that it takes 4 hours the outlet working alone to empty the cistern.

Answer: E.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135394 [1], given: 12691

2 KUDOS received
VP
VP
User avatar
S
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1354

Kudos [?]: 663 [2], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 09 Mar 2014, 10:11
2
This post received
KUDOS
Great explanation from Bunuel as usual.

Related alternative approach 1:
The first inlet fills up the cistern in 3 hours. Assume that the capacity of the cistern is 6L and therefore the rate of the first inlet is 2L/hr. The rate of the second inlet therefore becomes 1L/hr. The water contributed by both inlets in 2.5 hours (9:00 to 11:30am) = 2.5 (2+1) = 7.5L. As the cistern is just full in this time, the 1.5L over the 6L capacity must have been drained away by the outlet in one hour (10:30 to 110:30am). So the outlet will take 6/1.5 = 4 hours to drain the full cistern. Option (E).

Related alternative approach 2:
Lets calculate the time taken by the two inlets to fill the cistern. This comes out to be (6*3)/(6+3) = 2 hours. With the outlet open for one hour, the inlets take 2.5 hours to fill the cistern. This means
Volume of water flowing through the outlet in one hour = Volume of water flowing in through both the inlets in 0.5 hours
=> Vol of water flowing through the outlet in one hour = 0.5 (1/3 + 1/6) = 1/4 of the capacity of the cistern
=> Time taken to empty the cistern by the outlet working alone = 4 hours. Option (E).
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738


Last edited by GyanOne on 09 Mar 2014, 23:27, edited 1 time in total.

Kudos [?]: 663 [2], given: 20

1 KUDOS received
Manager
Manager
avatar
Joined: 01 May 2013
Posts: 62

Kudos [?]: 28 [1], given: 8

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 09 Mar 2014, 19:45
1
This post received
KUDOS
Bunuel wrote:

Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.

Letting x to be the rate of the outlet, we would have: 1/2 - x = 1/4 --> x = 1/4 cistern/hour, which means that it takes 4 hours the outlet working alone to empty the cistern.

Answer: E.

Hope it's clear.


This is right where I got stuck. I knew that it should have taken only 1/2 an hour to fill the remaining 1/4 of the cistern. Instead it took double the time.

Can you explain your last equation? I'm confused about exactly why 1/4 and 1/2 have this relationship. Thank you.

Edit:

Is this a good explanation? If it takes double the time, that means that really only 1/4 per hour is filled. The other 1/4 is "stolen" by the outlet. So that must be the rate that the outlet pumps. Therefore, it would take 4 hours.

Similarly, if instead we had inlets pumping at a rate of 1/2 per hour and they were slowed down to 1/3 per hour, the outlet would be stealing 1/6, so the full time it would take the outlet is 6 hours? Is that correct?

Kudos [?]: 28 [1], given: 8

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135394 [1], given: 12691

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 09 Mar 2014, 23:09
1
This post received
KUDOS
Expert's post
CCMBA wrote:
Bunuel wrote:

Then the outlet is turned on and the remaining 1/4 th of the cistern is filled in 1 hour.

Letting x to be the rate of the outlet, we would have: 1/2 - x = 1/4 --> x = 1/4 cistern/hour, which means that it takes 4 hours the outlet working alone to empty the cistern.

Answer: E.

Hope it's clear.


This is right where I got stuck. I knew that it should have taken only 1/2 an hour to fill the remaining 1/4 of the cistern. Instead it took double the time.

Can you explain your last equation? I'm confused about exactly why 1/4 and 1/2 have this relationship. Thank you.

Edit:

Is this a good explanation? If it takes double the time, that means that really only 1/4 per hour is filled. The other 1/4 is "stolen" by the outlet. So that must be the rate that the outlet pumps. Therefore, it would take 4 hours.

Similarly, if instead we had inlets pumping at a rate of 1/2 per hour and they were slowed down to 1/3 per hour, the outlet would be stealing 1/6, so the full time it would take the outlet is 6 hours? Is that correct?


Recall that we can sum/subtract the rates.

Inflow rate of the two inlets is 1/2 cistern/hour;
Outflow rate of the outlet is x cistern/hour;

Net inflow is 1/2 - x cistern/hour, hence 1/2 - x = 1/4.

Hope it helps.

P.S. Yes, your approach is correct.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135394 [1], given: 12691

Manager
Manager
avatar
Joined: 01 May 2013
Posts: 62

Kudos [?]: 28 [0], given: 8

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 10 Mar 2014, 10:17
Bunuel wrote:

Recall that we can sum/subtract the rates.

Inflow rate of the two inlets is 1/2 cistern/hour;
Outflow rate of the outlet is x cistern/hour;

Net inflow is 1/2 - x cistern/hour, hence 1/2 - x = 1/4.

Hope it helps.

P.S. Yes, your approach is correct.


Thank you so much! I have seen others use this approach on other Rate/Work problems, but I'm not sure I find all the formulas intuitive. I get this one now. Is there a comprehensive explanation of why we can use these shortcuts? I find that I have to reason through each individual problem, which is certainly inefficient.

Kudos [?]: 28 [0], given: 8

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135394 [1], given: 12691

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 10 Mar 2014, 10:36
1
This post received
KUDOS
Expert's post
CCMBA wrote:
Bunuel wrote:

Recall that we can sum/subtract the rates.

Inflow rate of the two inlets is 1/2 cistern/hour;
Outflow rate of the outlet is x cistern/hour;

Net inflow is 1/2 - x cistern/hour, hence 1/2 - x = 1/4.

Hope it helps.

P.S. Yes, your approach is correct.


Thank you so much! I have seen others use this approach on other Rate/Work problems, but I'm not sure I find all the formulas intuitive. I get this one now. Is there a comprehensive explanation of why we can use these shortcuts? I find that I have to reason through each individual problem, which is certainly inefficient.


THEORY
There are several important things you should know to solve work problems:

1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

\(time*speed=distance\) <--> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) --> \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) --> so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) --> so rate of 1 printer is \(rate=2\) pages per hour;

So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).

2. We can sum the rates.

If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together.

3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.

For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;

Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done
hours-to-type-pages-102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20R

Theory on work/rate problems: work-word-problems-made-easy-87357.html

All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66


Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135394 [1], given: 12691

Expert Post
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 548 [0], given: 16

Location: India
Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 10 Mar 2014, 20:10
Expert's post
1
This post was
BOOKMARKED
In the case of tank eventually filling, the formula is 1/ f1 + 1/f2 - 1/d = 1 /F
where f1 and f2 are the time taken by pipes 1 and 2 resp to fill, d is the time taken to drain and F is the total time taken to Fill.

Here f1 and f2 happen for 2.5 hrs and d happens for 1 hr. So the formula becomes,

1/f1 + 1/f2 - 1/(2.5 d) = 1/F
1/3 + 1/6 - 1/ 2.5d = 1/2.5
1/ 2.5d = 1/10
d= 4hrs
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Premium Material
Standardized Approaches

Kudos [?]: 548 [0], given: 16

1 KUDOS received
Manager
Manager
avatar
Joined: 07 Dec 2009
Posts: 107

Kudos [?]: 36 [1], given: 375

GMAT Date: 12-03-2014
GMAT ToolKit User Premium Member
Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 27 Jan 2015, 12:54
1
This post received
KUDOS
working together : I1 and I2 take 2 hrs to complete

Let the rate of 3rd Pipe be I3

2.5*(1/2) - (I3 * 1) = 1

I3 = 1/4

Ans 4 hrs

Kudos [?]: 36 [1], given: 375

Manager
Manager
avatar
Joined: 24 Nov 2013
Posts: 60

Kudos [?]: 19 [0], given: 115

Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 12 Sep 2015, 20:25
I approached it this way.
at 10.30am the inlets had completed 3/4 of the work of filling the cistern. 1/4 cistern is empty.
they were supposed to finish it by 11.00am.

However at 10.30am the outlet is turned on.

the result is that the cistern will now be full by 11.30am.
So the inlets end up working 30 mins more to nullify the effect of outlet working for 1 hour from 10.30am to 11.30am.

so the work done by outlet in 1 hr = work done by both inlets in 30 mins. = emptying / filling 1/4 of the cistern.
work done by outlet in 1 hr = 1/4 of the cistern.
hence outlet takes 4 hours to complete the work

Kudos [?]: 19 [0], given: 115

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14897

Kudos [?]: 287 [0], given: 0

Premium Member
Re: There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 19 Oct 2017, 14:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [0], given: 16

There are two inlets and one outlet to a cistern. One of the [#permalink]

Show Tags

New post 20 Oct 2017, 09:12
HarveyS wrote:
There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?

(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours


3/2 hour*1/2 combined rate=3/4 of cistern filled by 2 inlets together by 10:30
with no outlet running, 2 inlets would need another half hour to fill last 1/4
with outlet running from 10:30, 2 inlets need another hour to fill last 1/4
thus, outlet empties 1/4 of cistern in one hour,
and entire cistern in 4 hours
E

Kudos [?]: 291 [0], given: 16

There are two inlets and one outlet to a cistern. One of the   [#permalink] 20 Oct 2017, 09:12
Display posts from previous: Sort by

There are two inlets and one outlet to a cistern. One of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.