A and B can do a job in 12 days, B and C in 15 days and C and A in 20 days. How long would A take to do that work ?

Let the total work to be done = 60 units

Let rates at which A, B and C alone do the job be $$x$$ , $$y$$ and $$z$$ units/day respectively.

Rate at which A & B 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 A to finish the work = $$\frac{60}{2}$$ = 30 days