Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

Question: Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

Solution:
Worker A completes the task in 8 days. So, in one day, he will complete 1/8 part of the task.

So, A's one day work = 1/8
Similarly, B's one day work = 1/10

∴ (A+B)'s one day work = 1/8 + 1/10 = (5 + 4)/40 = 9/40

9/40 of the task is completed in one day so both will complete the whole task in 40/9 days