M and N can do a piece of work in16 days and O can do it in 48 days. In how many days will M,N, and O do this work together?

Given:

• M and N together can complete the work in 16 days.
• O alone can complete the work in 48 days.

Work done by M and N in 1 day = $\frac{1}{16}$

Work done by O in 1 day = $\frac{1}{48}$

Total work done together in 1 day:

$\frac{1}{16} + \frac{1}{48}$

Taking LCM = 48,

$\frac{3}{48} + \frac{1}{48} = \frac{4}{48} = \frac{1}{12}$

So, together they complete $\frac{1}{12}$ of the work in 1 day.

Therefore, total time taken = 12 days.