In how many days can both finish the work, working together?
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.

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