A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?

Question: A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?

Solution:
A's one day work = 1/30
A's ten-day work = (1/30) × 10 = 1/3

So the remaining work would be = 1 - 1/3 = 2/3

B's one day work = 1/20
A and B's one day work = 1/30 + 1/20 = (2 + 3)/60 = 5/60 = 1/12

1/12 of the job will be done by them in one day.
So, the remaining job 2/3 will be done in = (2/3) × 12 = 8 days

Therefore, the total number of days required to do the job would be = 10 + 8 = 18 days