both

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Thu Jun 17, 2010 12:44 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

OA: A

Last edited by gmatmachoman on Thu Jun 17, 2010 1:38 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Thu Jun 17, 2010 12:44 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Thu Jun 17, 2010 12:51 am

Assume 60 units of work..

A can do in 20 days means he does 3 units per day..
B can do in 30 days means he does 2 units per day..

they work togetehr, they do 5 units per day..

let us say it took D days to compete project
So 5(d-10)+2(10) = 60
therefore, d = 18

what is OA?

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Thu Jun 17, 2010 12:59 am

a in 1 day 1/20
b in 1 day 1/30
a+b in 1 day 1/20+1/30=1/12
so a+b together will complete work in 12 days
now a leave10 days before project is completed
so a+b work together for 2 days
in 2 days a+b will complete 1/12*2=1/6 work
so work remaining 1-1/6=5/6 of work
now b in 1 days does 1/30
so b will do 5/6 of work in another (5/6)/(1/30)=25 days
so project will be 25+2=27 days

Ideation without execution is delusion

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Thu Jun 17, 2010 1:12 am

amising6 wrote:a in 1 day 1/20
b in 1 day 1/30
a+b in 1 day 1/20+1/30=1/12
so a+b together will complete work in 12 days

Hi Aimsing6,

A left the work 10 days before the project completion date...
But not 10 days before expected completion date..

be careful about the detail!!

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Thu Jun 17, 2010 1:28 am

Both A and B can complete 1/12 unit of work in 1 day

For(d-10) days,they complete 1/12*(d-10) unit of work

Next 10 days B alone complete 1/3 work.

1/3+1/12(d-10)=1

d=18

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