A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?
Number of days A required do a piece of work : 14 days
Number of days B required do a piece of work : 21 days
Work done by A in one day: 
Work done by B in one day: 
Work done by A and B together in one day: 
= 
They can do the work together in 
days .
A and B worked together for 6 days, so work completed by A and B in 6 days : 
Work left = 
Number of days taken by B to complete the left over work : 
= 6 ( here 21 is days required by B to complete a piece of work).
Time taken to finish the work: 6 + 6 = 12 days.
Total time taken to finish the work: 12 days