It is currently 21 Sep 2017, 10:43

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Matt and Peter can do together a piece of work in 20 days

Author Message
TAGS:

### Hide Tags

Director
Joined: 05 Jan 2008
Posts: 687

Kudos [?]: 580 [1], given: 0

Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

11 Mar 2008, 03:56
1
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:27) correct 12% (01:50) wrong based on 371 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.

A. 26 days
B. 27 days
C. 23 days
D. 25 days
E. 24 days
[Reveal] Spoiler: OA

_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

Last edited by Bunuel on 23 Oct 2012, 05:22, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 580 [1], given: 0

Director
Joined: 10 Sep 2007
Posts: 936

Kudos [?]: 327 [0], given: 0

### Show Tags

11 Mar 2008, 07:13
1
This post was
BOOKMARKED
Suppose rate of work for per day Matt = M & Rate of work per day for Peter = P
Together in a Day they can finish = P + M units
Total Work Done in 20 Days = 20(P+M)
Total Work Done in 12 Days = 12(P+M)
Work Done by Peter in 10 Days = 10P

Since total work is same we can say that 20(P+M) = 12(P+M) + 10P => 8M = 2P => P = 4M
So total work done by them together in 20 Days = 20(4M+M) = 100M
Since Pete does 4M unit of work per day, it will take him 25 Days (100M/4M) to finish up the work.

Kudos [?]: 327 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1549

Kudos [?]: 173 [1], given: 2

### Show Tags

11 Mar 2008, 07:23
1
KUDOS
1
This post was
BOOKMARKED
together, they can do a piece in 20 days, i.e. 1/m + 1/p = 1/20

In 12 days, they can finish 12*(1/20) = 3/5 of the piece. After Matt leaves, 2/5 still needs to be done by Peter, which he does in 10 days.

10/(2/5) = 25

Kudos [?]: 173 [1], given: 2

Retired Moderator
Joined: 18 Jul 2008
Posts: 964

Kudos [?]: 285 [0], given: 5

### Show Tags

30 Mar 2009, 15:36
Isn't this the same question? time-work-61136.html#p442431 But why do the answers differ...

pmenon wrote:
together, they can do a piece in 20 days, i.e. 1/m + 1/p = 1/20

In 12 days, they can finish 12*(1/20) = 3/5 of the piece. After Matt leaves, 2/5 still needs to be done by Peter, which he does in 10 days.

10/(2/5) = 25

Kudos [?]: 285 [0], given: 5

Director
Joined: 14 Aug 2007
Posts: 726

Kudos [?]: 208 [0], given: 0

### Show Tags

01 Apr 2009, 00:06
Isn't this the same question? time-work-61136.html#p442431 But why do the answers differ...

Because Matt and Peter have some issues working together ..Just kidding.

Note that this problem is asking the the time taken by thr guy who did NOT stop working after 12 days while the question in link is asking the time taken by the guy who stopped working after 12 days.

Kudos [?]: 208 [0], given: 0

Manager
Joined: 14 Nov 2008
Posts: 195

Kudos [?]: 123 [0], given: 3

Schools: Stanford...Wait, I will come!!!

### Show Tags

01 Apr 2009, 00:49
Best way is this.
1) Get the unit of quantity of work. Make it a number which you find LCM of the given digits.
2) Calculate the rate of work for each person.
And then calculate what is asked.

So as per above,
Lets assume that 20*12=240 unit of work is there.
Assume rate of work per day for Matt is m, and for Peter is p;
so..
Matt and Peter can do together a piece of work in 20 days. implies..
(m+p)*20= 240
m+p=12
Now, peter works for 22 day while, matt works for 12 days.
so, 22p+12m=240
Solving the equations, we find the value of m and p as 2.4, and 9.6 unit of work/day respectively.
So peter will take, 240/9.6=25 days.

prasannar wrote:
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.

26days

27days

23days

25days

24 days

What is the best way to solve these problems?

Kudos [?]: 123 [0], given: 3

Intern
Joined: 11 Apr 2009
Posts: 1

Kudos [?]: 3 [3], given: 0

### Show Tags

11 Apr 2009, 22:10
3
KUDOS
Another easy way is ..

M&P complete 60% of the work in 12 days (since they complete 100% in 20 days)
P completes the remaining 40% in 10 days .. => to complete 100% he would need 25 days.

Kudos [?]: 3 [3], given: 0

Senior Manager
Joined: 28 Aug 2006
Posts: 303

Kudos [?]: 168 [0], given: 0

### Show Tags

12 Apr 2009, 04:36
Work done by M&P in 12 days = 12/20 = 3/5

Remaining 2/5 is done by P alone in 10 days.

So P alone can do the entire work in (5/2) X 10 = 25 days
_________________

Kudos [?]: 168 [0], given: 0

Manager
Joined: 13 Aug 2009
Posts: 199

Kudos [?]: 124 [0], given: 16

Schools: Sloan '14 (S)

### Show Tags

18 Aug 2009, 02:46
24.Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
26days
27days
23days
25days
24 days

Rate Together * # of days working together + Rate of Peter * # of days working alone = 1 completed job

let P = 3 of hours Peter can complete one job alone

(1/20)*12 + (1/P)*10 = 1

P = 25

Kudos [?]: 124 [0], given: 16

Intern
Joined: 02 Feb 2010
Posts: 2

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

### Show Tags

05 Feb 2010, 16:51
Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.

Peter completes the remaining (8/20) of the job in 10 days which means that the whole job(1) can be completed in X days.

<=> 8/20->10 <=> X=10/(8/20)= 25 Thus the answer is D.
1 -> X

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

Manager
Joined: 18 Jan 2012
Posts: 51

Kudos [?]: 102 [1], given: 26

Location: United States
Schools: IIM A '15 (A)
Re: Matt and Peter can do together a piece of work in 20 days. [#permalink]

### Show Tags

22 Oct 2012, 18:57
1
KUDOS
To me, the most intuitive approach to solve work /rate problems is to use smart numbers.
Then we need to find the work rate - work done each entity in 1 day. The subsequent steps are then very easy .

If 2 entities A and B work together, then Work done by A in one day + Work Done by B in one day = Total work done by A and B in one day.
Example - If a machine produces 10 widgets per day and another machine produces 20 widgets per day, then working together both machines can produce 30 (10 + 20) widgets per day.

Let's choose a nr that is divisible by all the numbers given in the question stem - 20,12,10
LCM of 20,12,10 = 60
Let's assume that Total work = 60 units.
Matt and Peter work together to complete the work in 20 days. So the work done by both of them together is 3 units per day (60/20)
Now we are almost done

Matt and Peter worked together for 12 days. Hence working together, they completed 12 x 3 = 36 units of work
What remains is 24 units and Peter completed this work all by himself in 10 days

Hence peter's work rate = 24/10 units per day

Therefore, Time taken by peter to complete the 60 units of work = Total Work /Peter's work rate = (60)/(24/10) = 25 days
_________________

-----------------------------------------------------------------------------------------------------
IT TAKES QUITE A BIT OF TIME AND TO POST DETAILED RESPONSES.
YOUR KUDOS IS VERY MUCH APPRECIATED

-----------------------------------------------------------------------------------------------------

Kudos [?]: 102 [1], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 41660

Kudos [?]: 124319 [2], given: 12077

Re: Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

23 Oct 2012, 05:27
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
prasannar wrote:
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.

A. 26 days
B. 27 days
C. 23 days
D. 25 days
E. 24 days

Matt and Peter together would complete 12/20=3/5th of the work in 12 days, thus the remaining 2/5th is done by Peter alone in 10 days.

Therefore Peter can complete the work alone in 10/(2/5)=25 days.

_________________

Kudos [?]: 124319 [2], given: 12077

Senior Manager
Joined: 13 Aug 2012
Posts: 462

Kudos [?]: 526 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

14 Nov 2012, 06:39
1
This post was
BOOKMARKED
$$\frac{1}{M}+\frac{1}{P}= \frac{1}{20}$$

Calculate work done together in 12 days:
$$\frac{1}{20}x12==>\frac{12}{20}=\frac{3}{5}$$

Remaining work is 1-3/5.
Calculate the days left for P to perform work alone:
$$\frac{1}{P}x10days=1-\frac{3}{5}$$
$$\frac{10}{P}=\frac{2}{5}$$
$$P=25 days$$

A. 26 days
B. 27 days
C. 23 days

D. 25 days
E. 24 days
_________________

Impossible is nothing to God.

Kudos [?]: 526 [0], given: 11

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17587

Kudos [?]: 270 [0], given: 0

Re: Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

27 Jan 2014, 12:57
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.
_________________

Kudos [?]: 270 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17587

Kudos [?]: 270 [0], given: 0

Re: Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

14 Feb 2015, 00:32
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.
_________________

Kudos [?]: 270 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17587

Kudos [?]: 270 [0], given: 0

Re: Matt and Peter can do together a piece of work in 20 days [#permalink]

### Show Tags

04 May 2016, 08:02
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.
_________________

Kudos [?]: 270 [0], given: 0

Re: Matt and Peter can do together a piece of work in 20 days   [#permalink] 04 May 2016, 08:02
Similar topics Replies Last post
Similar
Topics:
6 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 5 16 Apr 2017, 23:58
16 If 6 men can do a piece of work in 30 days of 9 hours each, 8 25 Sep 2016, 13:06
2 P,Q and R can do a piece of work in 4,6 and 12 days working 1 23 Oct 2013, 13:03
11 A and B can do a piece of work in 10 days, while B and C can do the sa 5 08 Nov 2016, 11:01
25 Micheal and Adam can do together a piece of work in 20 days. 9 10 Oct 2016, 06:48
Display posts from previous: Sort by

# Matt and Peter can do together a piece of work in 20 days

 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®.