A, B and C complete a work in 6, 8 and 12 days respectively. In how many days they can complete the work together.

\par A's one day's work =  \frac{1}{6}

\par B's one day's work =  \frac{1}{8}

\par C's one day's work =  \frac{1}{12}

\par (A + B + C)'s one day work = \frac{1}{6} + \frac{1}{8}+\frac{1}{12} = \frac{4+3+2}{24} = \frac{9}{24} = \frac{3}{8}

\par (A+B+C) will complete the work =  1\div \frac{3}{8} = \frac{8}{3} = 2\frac{2}{3}

\par \underline{Shortcut Method}

\frac{6\times 8\times 12}{6\times 8+6\times 12+8\times 12} = \frac{8}{3} = 2\frac{2}{3}                                          \lbrack \frac{t_{1 \times }t_{2 \times }t_{3}}{t_{1} t_{2}+t_{1} t_{3}+t_{2}t_{3}} \rbrack