Time and work

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mohitsharda: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Sat Aug 01, 2009 3:13 amFollowed by: 1 member; Thanked: 5 times; GMAT Score:740

by mohitsharda » Sun Aug 16, 2009 6:01 am

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

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Source: Beat The GMAT — Problem Solving | Sun Aug 16, 2009 6:01 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

Re: Time and work

by Morgoth » Sun Aug 16, 2009 7:55 am

mohitsharda 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

A's rate = 1/20
B's rate = 1/30

combine rate of A and B = 1/20 + 1/30 = 1/12

A and B can complete the entire work in 12 days

A quits 10 days before the work can be completed, this means A and B together worked for 2 days [12-10]

In 2 days A and B together completed = 2 * 1/12 = 1/6 of the total work
Work still needs to be completed = 1 -1/6 = 5/6

5/6 work will be completed by B alone = 5/6 / 1/30 = 25

Therefore, the work can be completed in 2+25 days = 27 days

Hence B.

Hope this helps.

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nano124: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Jun 20, 2009 2:57 pm

by nano124 » Sun Aug 16, 2009 10:11 am

Answer is B. If they were working together they would have completed the project in 12 days. However since A quit in 2 days we have 25/30th of the project that needs to be completed by B alone which will take 25 days. hence (A+B) + B = 2+25 or 27 days.

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Mon Aug 17, 2009 7:10 am

@ morgoth,
I think answer is A.
Since its written that A left 10 days before the project is completed, so during this time B worked alone. ie. 10/30=1/3 of the work is completed by B during last 10 days and 2/3rd of the work is completed by both A and B together which took 8 days.
i.e total of 8+10=18 days.
pls correct if I am wrong.
anyways whats the OA

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kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members; Thanked: 9 times

by kaulnikhil » Mon Aug 17, 2009 7:57 am

Got A ...wass the ans ???

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the_hustler: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Jul 14, 2009 7:28 am; Location: India

by the_hustler » Mon Aug 17, 2009 11:09 am

its A for sure.

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pandeyvineet24: Legendary Member; Posts: 527; Joined: Mon Jun 02, 2008 9:14 am; Location: Atlanta; Thanked: 17 times

by pandeyvineet24 » Mon Aug 17, 2009 12:05 pm

I got A as well.

Rate of A = 1/20, Rate of B = 1/30

Let the total time be T.

from the question
(T - 10)* (1/20) + T * (1/30) = 1

gives T = 18 days

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pandeyvineet24: Legendary Member; Posts: 527; Joined: Mon Jun 02, 2008 9:14 am; Location: Atlanta; Thanked: 17 times

by pandeyvineet24 » Mon Aug 17, 2009 12:05 pm

I got A as well.

Rate of A = 1/20, Rate of B = 1/30

Let the total time be T.

from the question
(T - 10)* (1/20) + T * (1/30) = 1

gives T = 18 days

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thestartupguy: Master | Next Rank: 500 Posts; Posts: 150; Joined: Thu May 05, 2011 10:04 amFollowed by: 4 members; Thanked: 5 times

by thestartupguy » Sat Sep 17, 2011 10:56 am

@pandeyvineet

Rate of A = 1/20, Rate of B = 1/30

Let the total time be T.

from the question
(T - 10)* (1/20) + T * (1/30) = 1

gives T = 18 days

The highlighted text should be 1/12 coz. A and B work together for the first two days.

So the answer will be 27 days.

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sat Sep 17, 2011 11:05 am

Rate of A =1/20. Rate of B=1/30

Combined rate of A and B = 1/20+1/30 = 1/12

Entire work completed by both A and B in 12 days

As A leaves 10 days before that means, A and B worked together for the first 2 days

In 2 days, together they completed 2/12 = 1/6

Remaining work to be completed by B is 5/6

Time taken by B is 5/6/1/30 = 25

Total completion time is 25+2 = 27

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sat Sep 17, 2011 12:34 pm

@sl750 and msr4mba. Your answers are wrong. Check this link

https://www.beatthegmat.com/a-quits-befo ... t=New-York

Both Mitch and Anurag have solved it.

Here is my solution:
Let the work to be done be the typing of 60 pages
A
Time=20days
Rate=60/20= 3pages/Day

B
Time=30days
Rate=60/30=2pages/Day

Now let the time for which B works equal x i.e. from the beginning to end. The work done by B is 2x (Work=Rate*Time). Since A quit 10 days prior to the end the time he worked for is
x-10 so the work done by him is 3(x-10)

Work Done by A+Work Done by B=60
2x+3x-30=60
x=18

Hence A

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Sep 18, 2011 3:58 am

For those who got 27 days:

If A leaves 10 days before the job is completed, it is not possible that B works for 25 days after A leaves.
The two times (10 days and 25 days) contradict each other.

To guarantee that B works for exactly 10 days on his own, first determine how much work B completes in 10 days.
Then calculate how much time is needed for A and B to complete the remaining work.

This problem is no different from the following:
B works alone for 10 days.
Then A and B work together to complete the job.
What is the total number of days that B works?

I posted a solution here:

https://www.beatthegmat.com/a-quits-befo ... t=New-York.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Sep 18, 2011 4:45 am

mohitsharda 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

Let the total work be of 60 units ( LCM of the Time Taken by A & B)

Efficiency of A is 3 units

Efficiency of B is 2 units

Together the produce 5 units

Let A and B works together for ' d ' days

So together the complete 5d units of work

B does the rest of the work ( ie for 10 days ) , so work done by B is 20 units

Now 5d + 20 = 60

So 5d = 40

and d = 8

Hence A and B worked for 8 days and B alone worked for 10 days , they worked 18 days in all....

Abhishek

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