A and B together can do a piece of work in 10 days, B and C together can doit in 15 days while C and A together can do it in 20 days. They work together for 8 days. C alone will complete the remaining work in:

Total work = L.C.M of 10, 15 and 20 = 60 units

(A + B)’s 1 day work = 60/10 = 6 units ------i

(B + C)’s 1 day work = 60/15 = 4 units ------ii

(A + C)’s 1 day work = 60/20 = 3 units ------iii

2 (A + B + C)’s 1 day work = 13 units

(A + B + C)’s 1 day work = 13/2 units ------------iv

From i and iv

C's 1 day work = $$\frac{13}{2}-6=\frac{1}{2}$$

(A+B+C)'s 8 day work = $$\frac{13}{2}\times\ 8=52$$ units

Remaining work = 60 - 52= 8 units.

So, C can do remaining work = $$8\times2=16\ $$ days.