A can do a 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?

Let the rate of work done by A and B $$ \frac{1}{A} and \frac{1}{B} $$
$$\frac{1}{A} = \frac{1}{12}$$
Work done by A in 3 days = $$3 \times \frac{1}{A} = \frac{3}{12} = \frac{1}{4}$$
In 3 more days A and B together completed the remaining $$ \frac{3}{4}$$th of the work.
$$3 \times (\frac{1}{A} + \frac{1}{B}) = \frac{3}{4}$$
$$ (\frac{1}{A} + \frac{1}{B}) = \frac{1}{4}$$
$$ (\frac{1}{12} + \frac{1}{B}) = \frac{1}{4}$$
$$ \frac{1}{B}= \frac{1}{4} - \frac{1}{12}$$
$$ \frac{1}{B}= \frac{3-1}{12} = \frac{2}{12} = \frac{1}{6} $$
B alone can complete the work in 6 days.
Hence Option A is the correct answer.