It is currently 17 Nov 2017, 16:45

### 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

# A can complete a project in 20 days and B can complete the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Sep 2012
Posts: 32

Kudos [?]: 41 [4], given: 33

Location: United States
A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 05:16
4
KUDOS
27
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

53% (01:39) correct 47% (02:04) wrong based on 503 sessions

### HideShow timer Statistics

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days
[Reveal] Spoiler: OA

Kudos [?]: 41 [4], given: 33

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [8], given: 12324

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 05:35
8
KUDOS
Expert's post
4
This post was
BOOKMARKED
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.
_________________

Kudos [?]: 132517 [8], given: 12324

Manager
Joined: 05 Jul 2012
Posts: 76

Kudos [?]: 52 [1], given: 8

Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 05:49
1
KUDOS
2
This post was
BOOKMARKED
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

Assume to total work to be 60 Units ( LCM of 20 & 30)
A does 3 units per day ( =60/20)
B does 2 units per day ( =60/30)
B works for 10 days alone work done = 2*10 = 20 units
A and B work together for the rest of the time
work left = 40 units
A and b together to 5 units oer day ( 2+3 = 5)
days required to do 40 units = 40/5 = 8

Total = 10+8 = 18

Kudos [?]: 52 [1], given: 8

Intern
Joined: 09 Sep 2012
Posts: 32

Kudos [?]: 41 [1], given: 33

Location: United States
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 06:00
1
KUDOS
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

Kudos [?]: 41 [1], given: 33

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [7], given: 12324

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 06:13
7
KUDOS
Expert's post
4
This post was
BOOKMARKED
154238 wrote:
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

Yes, working together they can complete the job in 12 days, but if A leaves at some point, then they no longer will need 12 days, they will need more. So, you cannot say that they worked together for 12-10=2 days.

Consider another approach:

In 10 days that B worked alone 10*1/30=1/3 of the job was done and 2/3 of the job was left to be done by A and B together.

Rate*Time=Job Done --> (1/20+1/30)*Time=2/3 --> Time=8. So, they worked together for 8 days, which means that total time is 10+8=18 days.

Hope it helps.
_________________

Kudos [?]: 132517 [7], given: 12324

Manager
Joined: 25 Jun 2012
Posts: 70

Kudos [?]: 134 [0], given: 21

Location: India
WE: General Management (Energy and Utilities)
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

21 Sep 2012, 10:26
A = w/20
B = w/30

A+B = w/20+w/30

Rate*Time = Work
(A+B)* (t-10) = W (A left the job 10 days before the total day)

solving we get t=28 days

putting total days = y-10= 28-10 = 18 days

I think I am wrong somewhere...

Kudos [?]: 134 [0], given: 21

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 556 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

14 Nov 2012, 07:08
d is the total days to complete the project.
A worked for d-10 days while b worked the whole d days.

Setup the Rate Equation like this $$(Rate of A) (d -10) + (Rate of B) (d) = 1$$

$$(\frac{1}{20}) (d-10) + (\frac{1}{30}) d = 1$$, 1 represents 100% of the project
$$3d -30 + 2d = 60 ==> 5d = 90 ==> d = 18 days$$

_________________

Impossible is nothing to God.

Kudos [?]: 556 [0], given: 11

Manager
Joined: 27 May 2014
Posts: 87

Kudos [?]: 20 [0], given: 21

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

11 Oct 2014, 12:12
I used logic and back solved to get this answer. We know the combined rate 12 days (1/30) + (1/20). So eliminate choice E as we know that A is stopping ten days earlier. Next look at 28 days and the 26.67 days. If we were to subtract 10 from each we would get something greater than 12 days, so we can eliminate those because if they worked together for more than 12 days the project would be complete. Next I looked at the 16 days subtracted out 10 days do this means they worked together for six days, completing half of the work (6 * (1/12)) and b would have 10 days (1/30) to complete the other half which is obviously not possible. Hence 18 is the answer

Kudos [?]: 20 [0], given: 21

Non-Human User
Joined: 09 Sep 2013
Posts: 15707

Kudos [?]: 281 [0], given: 0

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

24 Feb 2016, 04:53
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 [?]: 281 [0], given: 0

Intern
Joined: 01 Feb 2016
Posts: 9

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

Location: Viet Nam
GMAT 1: 500 Q49 V15
GMAT 2: 680 Q49 V34
WE: Real Estate (Real Estate)
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

24 Feb 2016, 11:19
A -> 1 day does 1/20 jobs
B -> 1 day does 1/30 jobs
=> (1/20+1/30)*t + 10*1/30=1 -> t=8 -> Time: 8+10=18 -> A

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

Director
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 534 [0], given: 16

Location: India
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

05 Jun 2017, 19:11
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

1. (no.of days worked by A)/ (time normally taken by A working alone) + (no.of days worked by B)/ (time normally taken by B working alone) =1
2. Let B work on the project for x days which is also the time for completion of the project
3. (x-10)/20 +x/30 = 1, So x=18 days
_________________

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

Standardized Approaches

Kudos [?]: 534 [0], given: 16

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 900 [0], given: 5

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

08 Jun 2017, 16:48
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

We are given that A can complete a project in 20 days and B can complete the same project in 30 days. Thus, the rate of A is 1/20 and the rate of B is 1/30. Since A quits 10 days before the project is completed, we can let t = the time in days worked by B, and thus, (t - 10) = the time in days worked by A. To determine t, we calculate the work done by A and the work done by B, using the work formula: work = rate x time.

work of A + work of B = 1

(1/20)(t - 10) + (1/30)(t) = 1

(t - 10)/20 + t/30 = 1

Multiplying the entire equation by 60, we have:

3t - 30 + 2t = 60

5t = 90

t = 18

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 900 [0], given: 5

Manager
Joined: 30 Jul 2014
Posts: 136

Kudos [?]: 11 [0], given: 98

GPA: 3.72
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

11 Sep 2017, 06:14
I did a very silly calculation mistake in this question-
(3+2)(x-10) + 2*10 = 60 should give us the number of days...
_________________

A lot needs to be learned from all of you.

Kudos [?]: 11 [0], given: 98

Manager
Joined: 02 Feb 2016
Posts: 90

Kudos [?]: 5 [0], given: 40

GMAT 1: 690 Q43 V41
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

20 Sep 2017, 11:51
Bunuel wrote:
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.

Hi Bunuel,

I understand the method but when I applied this on my own, I placed 1/T on the RHS of the equation instead of 1. Can you please help me understand why do we have 1 instead of 1/T on RHS?

Kudos [?]: 5 [0], given: 40

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [0], given: 12324

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

20 Sep 2017, 11:58
TheMastermind wrote:
Bunuel wrote:
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.

Hi Bunuel,

I understand the method but when I applied this on my own, I placed 1/T on the RHS of the equation instead of 1. Can you please help me understand why do we have 1 instead of 1/T on RHS?

1/t is 1/(time), so rate.

The left hand side is (rate)(time) + (rate)(time) = (job done) + (job done) so it cannot equal to (rate), it should be the total (job done), which is 1.
_________________

Kudos [?]: 132517 [0], given: 12324

Intern
Joined: 11 Sep 2017
Posts: 3

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

A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

20 Sep 2017, 13:38
[quote="154238"]A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

In 10 days B can do 1/3 of work

So A and B together have to do 2/3 of work

X(1/12) = 2/3
X= 8

So total 18 days.

Good question

Sent from my iPhone using GMAT Club Forum mobile app

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

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4773

Kudos [?]: 3783 [0], given: 2445

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

27 Sep 2017, 18:32
A completes a project in 20 days which means A completes 5% of the project in a day.

B completes the same project in 30 days which means A completes 3.34% of the project in a day.

In a day, A&B together completes 8.34% of the project.

A quits 10 days before the project is completed, which means B completed 33.4% of the project on his own (10 days * 3.34% each day)

Therefore A&B together completed 66.6% of the project, so they must have worked for 8 days together. (66.6% / 8.34%)

So total time to finish the project = 10 + 8 = 18 days.
_________________

Kudos [?]: 3783 [0], given: 2445

Intern
Joined: 10 Sep 2017
Posts: 11

Kudos [?]: 1 [0], given: 10

Concentration: Operations, Organizational Behavior
Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

28 Sep 2017, 22:28
154238 wrote:
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

This is the same problem I'm dealing with.

Kudos [?]: 1 [0], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [0], given: 12324

Re: A can complete a project in 20 days and B can complete the [#permalink]

### Show Tags

28 Sep 2017, 23:28
Jashan79 wrote:
154238 wrote:
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

This is the same problem I'm dealing with.

_________________

Kudos [?]: 132517 [0], given: 12324

Re: A can complete a project in 20 days and B can complete the   [#permalink] 28 Sep 2017, 23:28
Display posts from previous: Sort by