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

LCM of (12,15,20 ) = 60

let assume that total 60 units of work is there

Given that (A+B) together takes 12 days to complete 60 units of work

and hence (A+B)'s 1 day work = 5 unit............(1)

Given that (B + C) together takes 15 days to complete 60 units of work

and hence (B + C)'s 1 day work = 4 unit.............(2)

Given that (C + A) together takes 20 days to complete 60 units of work

and hence (A + C)'s 1 day work = 3 unit...........(3)

Adding equation 1, 2, 3

2(A+B+C) = 12 units

So , (A+B+C)'s 1 day work = 6 unit ......(4)

From equation 2 and 4

A's 1 day work = 2 units

hence A will take= $$\frac{60}{2}$$ = 30 days