Question

A can do a piece of work in 20 days, b in 30 days and c in 60 days. all of them began to work together. however a left the job after 6 days and b quit work 6 days before the completion of work. how many days did the work last?

Answer 1

A can do a piece of work in 20 days
so, work percentage of A = 100%/20 = 5%

B can do a piece of work in 30 days
so, work percentage of B = 100%/30 = 3.33%

C can do a piece of work in 60 days
so, work percentage of C = 100%/60 = 1.66%

A left the job after 6 days
work percentage of A , B and C do job in 6 days = (5% + 3.33% + 1.66%) × 6 = 10% × 6 = 60%

B quit work 6 days before the completion
work percentage of C of last 6 days = 6 × 1.666% = 10%
so, last 6 days C can do 10% work and remaining 100% - 60% - 10% = 30%

so, 30% of work done by B and C
no of days B and C work together = ( 30%/(3.33% + 1.66%)) = 30%/5% = 6 days

work last for 6+6+6 = 18 days

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