A piece of work can be done by Ram and Shyam in 12 days, by Shyam and Hari in 15 days and by Hari and Ram in 20 days. Ram alone will complete the work in

Let the total work to be done = 60 units

Let rates at which Ram, Shyam and Hari alone do the job be $$x$$ , $$y$$ and $$z$$ units/day respectively.

Rate at which Ram & Shyam completes the work = $$\frac{60}{12}$$ = 5

=> $$x + y = 5$$

Similarly, $$y + z = 4$$

and $$z + x = 3$$

Adding all the above equations, we get :

=> $$2(x + y + z) = 12$$

=> $$x + y + z = 6$$

Substituting value of $$(y + z)$$ in above equation, we get $$x = 6-4 = 2$$

=> No. of days required by Ram to finish the work = $$\frac{60}{2}$$ = 30 days