Q: If A and B can complete a piece of work in 4 days and A can complete the same work in 12 days, how many days would it take for B to complete the work alone?  

Answer: A

A and B together can complete the work in 4 days,
so the amount of work they complete in 1 day is (1/4) of the total work.
A alone can complete the work in 12 days, so the amount of work he completes in 1 day is (1/12) of the total work.
The amount of work B completes in 1 day is the total amount of work completed by A and B in 1 day minus the amount of work A completes in 1 day.
This is (1/4) - (1/12) = (1/6) of the total work.
Since B completes (1/6) of the total work in 1 day, it will take him 6 days to complete the entire work.

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