A and B can do a piece of work in 10 days. B and C together can do it in 15 days. If A is twice as good a workman as C. Find what time B alone can do it?

Assume that A, B and C can do $$a$$, $$b$$ and $$c$$ units of work per day.

So, the total work is $$10\times\left(a+b\right)=10a+10b$$ . . . (1)

Similarly, the total work is $$15\times\left(b+c\right)=15b+15c$$ . . . (2)

Equate eqn(1) and eqn (2) we get

$$10a+10b=15b+15c$$

Given that A is twice as good a workman as C or $$a=2c$$

Putting in above equation we get

$$20c+10b=15b+15c$$

or, $$5c=5b$$

or, $$b=c$$

So, the efficiency of B and C is the same

If they together complete the work in 15 days, B alone will complete it in 30 days.