A can do a piece of work in 12 days. When he had worked for 3 days. B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work ?

Answer: Option A

Total work = 12
Efficiency 1 units/day = 12 days time (A)
After 3 days A finishes 3 units.
∴ Work left =12 - 3 = 9 units
9 units of work, 3 units/day = 3 days (A + B)
(A + B)'s one day work = 3 units
A's one day work = 1 unit
B's one day work = 3 - 1 = 2 units
∴ B completes whole work in
$$\begin{array}{rl}& =\frac{\text{Total work}}{\text{Efficiency}}\\ & =\frac{12}{2}\\ & =\text{6 days }\end{array}$$