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?
A's one day work=1/14
B's one day work=1/21
{A+B} one day work=1/14+1/21=5/42
they both work 6 day =5/42*6=5/7
B had to complete the remainig work=1-5/7=2/7
B had to complete the work=2/7 is divided by 1/21
divide change into mutiply=2/7*21/1=6
total time taken =6+6=12