A and B can do a job alone in 20 days
and 30 days respectively. In
how many days the job will be finished
if A and B work together
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A completes the work in 30 days -> In 1 day he completes 1/30 part of job.
B completes the work in 20 days -> In 1 day he completes 1/20 part of job.
Work done by A & B both in 1 day= 1/30 + 1/20
=(20+30)/(20x30) = 5/60 = 1/12
Let both A & B workd for 'x' days.
Work done by them in x day = x/12
Remaining work = 1-x/12 ………(1)
This remaining work is done by A alone in 5 days.
Hence,
Work done by A in 5 days = Remaining work
5/30 = 1-x/12 …. From (1)
x/12 = 1–1/6
x = (5x12)/6
x=10
Total number of days to complete work = 10+5 = 15 days
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