A can do three-fourth of a work in 12 days and B can do four-fifth of the same work in 20 days. In how many days can they complete the whole work, working together?

Time taken by A to complete the whole work:
$$\frac{3}{4}\text{ of work}=12\text{ days}⟹\text{Total work}=12\times \frac{4}{3}=16\text{ days}$$
Time taken by B to complete the whole work:
$$\frac{4}{5}\text{ of work}=20\text{ days}⟹\text{Total work}=20\times \frac{5}{4}=25\text{ days}$$
Let total work be the LCM of 16 and 25 = $400$ units.Efficiency of A = $\frac{400}{16}=25$ units/dayEfficiency of B = $\frac{400}{25}=16$ units/dayCombined efficiency of A and B = $25+16=41$ units/dayTime taken together:
$$\text{Time}=\frac{400}{41}=9\frac{31}{41}\text{ days}$$