Question:
A can do $\frac{2}{3}$ of a certain work in 16 days and $B$ can do $\frac{1}{4}$ of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do $\frac{2}{3}$ work in 16 days
So, work done by A in one day $=\frac{2}{48}=\frac{1}{24}$
B can do $\frac{1}{4}$ work in 3 days
So, work done by B in one day $=\frac{1}{12}$
Work done jointly by $\mathrm{A}$ and $\mathrm{B}$ in one day $=\frac{1}{24}+\frac{1}{12}=\frac{1+2}{24}=\frac{3}{24}=\frac{1}{8}$
So, $\mathrm{A}$ and $\mathrm{B}$ together will take 8 days to complete the work.