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

$\par&space;A's&space;one&space;day's&space;work&space;=$  $\frac{1}{6}$

$\par&space;B's&space;one&space;day's&space;work&space;=$  $\frac{1}{8}$

$\par&space;C's&space;one&space;day's&space;work&space;=$  $\frac{1}{12}$

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

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

$\par&space;\underline{Shortcut&space;Method}$

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