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 total work be 1 unit

Let rate at which 1 man do the work = $$x$$ units/day

The rate at which 1 boy do the work = $$y$$ units/day

=> Rate at which 2 men and 3 boys do the work = $$\frac{1}{10}$$ units/day

=> $$2x + 3y = \frac{1}{10}$$

Also, rate at which 3 men and 2 boys do the work = $$\frac{1}{8}$$ units/day

=> $$3x + 2y = \frac{1}{8}$$

Solving above equations, we get :

$$x = \frac{7}{200}$$ & $$y = \frac{1}{100}$$

To find = $$2x + y$$

= $$\frac{7}{100} + \frac{1}{100} = \frac{8}{100}$$

$$\therefore$$ No. of days required for 2 men and 1 boy to finish the work = $$\frac{1}{\frac{8}{100}} = \frac{100}{8}$$

= 12.5 days