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rate and work

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rate and work

by gmatnmein2010 » Mon Feb 08, 2010 5:35 am
A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
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by harsh.champ » Mon Feb 08, 2010 6:01 am
gmatnmein2010 wrote:A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Let an imaginary unit be 110 works.
1 man will complete the 110works in 1100 days.Hence, in 1 day only 0.1work
Till day 60 work done = 60works.
Now,50 works left.
6 more ppl hired.Hence,16 man crew so works done in 1 day = 16x0.1 = 1.6works
Hence,days required = 50/1.6=31.25 which is 32.
so,92 days .
hence [spoiler]8(100-92) E.[/spoiler]
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by thephoenix » Mon Feb 08, 2010 6:19 am
the job was finish by 10 people 110 days.
nowon the 61-st day, after 5 days of rain --> 5 days was rain,
--->55 days they worked ---> they completed 55/110 =1/2 of the job
1/2 is left =55 days of work for 10 people

Now 6 more people was hired -->
10 people in 1 day does sme workand
16 people in 1 day does =16/10 of the same work
hence speed of construction increased by 1.6,
now days needed to finish 55/1.6=34.375,
BUT after they were hired job was done in 100-60=40 days -->
--->approx 5-6 days rained.
They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 in(40) days.
hence day rain=5 days
HTH
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