A can do a work in 40 days and B can do the same work in 60 days. How long will it take together to complete the work.

One day work of $A=\frac{1}{40}$

One day work of$B=\frac{1}{60}$

The work in $\Rightarrow \frac{1}{40}+\frac{1}{60}\Rightarrow \frac{3+2}{120}$

A & B's Efficiency $=\frac{1}{24}$

The work will be completed in 24 days