Question

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?

Answer 1

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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