A can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?
Given that, A can do a task in 8 days.
∴ 1 day’s work by A = 1/8
Also, B can do it in 10 days
∴ 1 day’s work by B = 1/10
1 day’s work by both A and B together = $(\frac{1}{8}\; + \;\frac{1}{{10}}\; = \;\frac{{5\; + \;4}}{{40}}\; = \;\frac{9}{{40}})$
To do the whole work, time taken by A and B together = $(\frac{1}{{\frac{9}{{40}}}}\; = \;\frac{{40}}{9})$