If 8 men or 12 boys can do a piece of work in 16 days, the number of days required to complete the work by 20 men and 6 boys is

Let assume the amount of work be 48 units (which is LCM of 8,12,16)

It is given that 8 men can do 48 units of work in = 16 days

then 1 men's 1 day work = $$\frac{3}{8}$$ units

20 men's 1 day work = 20 x $$\frac{3}{8}$$ = 7.5 units

Now it is also given that 12 boys do the same amount of work of 48 units in = 16 days

so, 1 boy's 1 day work = $$\frac{1}{4}$$ units

6 boy's 1 day work = $$\frac{3}{2}$$ units = 1.5 units

Now , (20 men + 6 boy) 's 1 day work = 7.5 + 1.5 = 9 units

So, number of days required by (20 men + 6 boy) to complete 48 units of work = $$\frac{48}{9}$$ = 5 $$\frac{1}{3}$$ days