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.

$\par&space;A's&space;one&space;day's&space;work&space;=$  $\frac{1}{20}$

$\par&space;B's&space;one&space;day's&space;work&space;=$  $\frac{1}{30}$

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

$\par&space;A&space;and&space;B&space;can&space;complete&space;the&space;work&space;in&space;12&space;days$

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

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

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

$\frac{20&space;\times&space;30}{20+50}$ $=&space;\frac{600}{50}&space;=&space;12$