a company has a job to prepare certain number of cans and there are three machines a, b and c for this job. a can complete the job in 3 days, b can complete the job in 4 days and c can complete the job in 6 days. how many days the company will it take to complete the job if all the machines are used simultaneously?
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let the complete job be represented by W
job done by A in 3 days = W
job done by A in 1 day = W/3
job done by B in 4 days = W
job done by B in 1 day = W/4
job done by C in 6 days = W
job done by C in one day = W/6
if A , B , C works at a same time
then work done by A , B , C together in one day = W/3 + W/4 + W/6
= (4W + 3W+2W)/12 = 9W/12 = 3W/4
no. of days required by A , B , B togther to complete work W
= Total work/ work done by A , B , C together in one day
= W / ( 3W/4) = 4/3 days
hence if all three machines are used simultaneously , work will be completed in 4/3 days that is 1.33 days.
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