A does 30% of a work in 30 days. He then calls in B and they together finish the remaining work in 20 days. How long B alone would take to do the whole work?

Let total work to be done = 100 units

Work done by A in 30 days = $$\frac{30}{100} \times 100 = 30$$ units

A's efficiency = $$\frac{30}{30} = 1$$ unit/day

Remaining work = 100 - 30 = 70 units

Let B's efficiency = $$x$$ units/day

Now, A and B complete remaining work in 20 days

=> $$(1 + x) \times 20 = 70$$

=> $$1 + x = \frac{70}{20} = 3.5$$

=> $$x = 3.5 - 1 = 2.5$$

$$\therefore$$ Time taken by B to complete the whole work alone = $$\frac{100}{2.5} = 40$$ days

=> Ans - (A)