2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?

Let the amount work equivalent to 40 units (LCM of 10 and 8)

It is given that 2 men and 3 boys can do 40 units of work in = 10 days

(2 men + 3 boys)'s 1 day work = 4 units ........(1)

It is given that 3 men and 2 boys can do 40 units of work in = 8 days

(3 men + 2 boys)'s 1 day work = 5 units ............(2)

From equation 1 and 2

1 boy' 1 day work = $$\frac{2}{5}$$ units

1 man's 1 day work = $$\frac{7}{5}$$ units

(2 men + 1 boy)'s 1 day work = $$\frac{16}{5}$$ units

So, number of days required by (2 men + 1 boy) to complete 40 units of work = $$\frac{40 \times 5}{16}$$ = 12.5 days