A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

Explanation:-

Formula: If A can do a piece of work in n days, then A's 1 day's work = $$\frac{1}{{\text{n}}}$$
$$\eqalign{ & (A + B + C)'s\,1\,{\text{day's work}} \cr & = \left( {\frac{1}{{24}} + \frac{1}{6} + \frac{1}{{12}}} \right) = \frac{7}{{24}} \cr}$$
Formula: If A's 1 day's work = $$\frac{1}{{\text{n}}}$$ , then A can finish the work in n days
So, all the three together will complete the job in
$$\left( {\frac{{24}}{7}} \right){\text{days}} = 3\frac{3}{7}{\text{days}}$$