A can do (1/3) of a work in 5 days and B can do (2/5) of the work in 10 days. In how many days both A and B together can do the work?

∵ 1/3 of work is done by A in 5 days.
∴ Whole work will be done by A in 15 days.
∵ 2/3 of work is done by B in 10 days.
Whole work will be done by B in 10 x (5/2) i.e., 25days
∴ (A + B)'s 1 day's work = (1/15 + 1/25) = 8/75
So, both together can finish it in 75/8 days, i.e., 9³/₈days.