B does 50% of a work in 20 days. C joins B and they together finish the remaining work in 4 days. C alone can do the whole work in days.

B does 50% of a work in 20 days.

means $$\frac{1}{2}$$ work = 20 days

So 

B does 100% of a work in 40 days.

C joins B and they together finish the remaining work ($$\frac{1}{2}$$ work left)in 4 days

C joins B and they together finish the 100% work in 8 days  

B = 40

C + B = 8

lcm = total work = 40

efficiency of B = 1

efficiency ofB +   C = 5

so  C efficiency = 5-1 = 4

C alone can do the whole work in = $$\frac {40}{4}$$ = 10 days