A and B can do a job in 25 days. after 15 days of working together B leaves. if A completes the remaining part of the job in 20 days. how long would it take to complete the job working separately?
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A and B can do (1/25)th part of the work in a day.
In 15 days that A and B worked together they completed (15/25) or (3/5)th of the work and what remained was (2/5)th of the work.
A completed the (2/5)th part of the work in 20 days. So A would have taken 20/(2/5) = 50 days to complete the work, working alone.
B alone does (1/25)-(1/50) = (1/50)th of the work in a day.
So A and B would both take 50 days to the same work, working alone.
Check: In 15 days A and B did 15[(1/50+(1/50)] = 15*2/50 = 3/5th of the work. and the remaining (2/5) took A (2/5)*50 = 20 days. Correct.
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