SOLUTION: A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work?

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Question 394478: A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work?
Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A piece of work can be done in 48 days by 40 men.
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Each day 1/48 th of the job was done by 40 men
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Each man did (1/(48*40)th = 1/1920th of the job.
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After 15 days, 16 men were transferred.
In 15 days 15/1920 th of the job was done.
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There still remained 1905/1920 th of the job to be done.
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In how many days can the remaining men finish the work?
There are now 24 men working.
Each day 24/1020 th of the job is done
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# of days required is (amt of work to do)/(amt of work done in a day by 24 men)
= [1905/1920]/[24/1020] = 1905/24 = 79.375 days
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Cheers,
Stan H.

Answer by jrfrunner(365) (Show Source):
You can put this solution on YOUR website!
A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work?
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40 men can do the job in 48 days, this means that 40 men can do 1/48 of the job each hour
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after 15 hours: 15/48 of the job is completed and 33/48=11/16 of the job incomplete
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16 men are transferred. That leaves 24 men to complete the job.
each man worked at a rate of 1/(48*40) (assuming they all work at the same rate).
So the remaining 24 men work at the rate of 24/(48*40)=1/80
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11/16 of the job needs to be done by a crew of 24 working at a rate of 1/80 per hour.
Job=rate *time or time =job/rate=(11/16)/1/80)=80*11/16=55hours