A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task along to the number of days taken by B when completing the same task alone?

Let the work completed by A in one day = $$\frac{1}{A}$$
Let the work completed by B in one day = $$\frac{1}{B}$$
Let the work completed by C in one day = $$\frac{1}{C}$$
$$\frac{1}{A}$$ + $$\frac{1}{B}$$ = $$\frac{1}{20}$$
$$\frac{1}{B}$$ + $$\frac{1}{C}$$ = $$\frac{1}{30}$$
$$\frac{1}{A}$$ + $$\frac{1}{C}$$ = $$\frac{1}{40}$$
Solving the above equations we get $$\frac{1}{A}$$ = $$\frac{1}{24}$$ 

$$\frac{1}{B}$$ = $$\frac{1}{20}-\frac{1}{24}$$ = $$\frac{1}{120}$$