Question

A can do a piece of work in 14 days while B can do it in 21 days they began together and work 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

Answer 1

A's one day work = 1/14
B's one day work = 1/21

A and B 's one day work = (1/14) +(1/21)
They worked for 6 days = 6((1/14) +(1/21))
                                        = 35/49
Remaining work ⇒ 1 - 35/49 
let B alone completed the remaining work in x days
remaining work to be completed by B x(1/21) = 1 - 35/49
                                                                 x(1/21) = 14/49
                                                                          x = 6

∴B alone finish the remaining work in 6 days

Answer 2

b can complete it in 14 days