A can do a work in 20 days and B in 30 days. In how many days they can complete the work if they work together.

\par A's one day's work =  \frac{1}{20}

\par B's one day's work =  \frac{1}{30}

\par (A + B)'s one day work = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12}

\par A and B can complete the work in 12 days

 

\par \underline{Shortcut Method}

 

\par If A can do a work in t_{1} \par days and B can do it in t_{2}$ days

\par then A and B Together can do same work in \frac{t_{1 \times } t _ {2}}{t_{1}+ t_{2}} days.

\frac{20 \times 30}{20+50} = \frac{600}{50} = 12