To do a certain work, the ratio of efficiencies of A and B is 3 : 7. Working together, they can complete a work in 14 days. B started the work and after working for 8 days, he left and A completed the remaining work. For how many days did A work?

28

Given, 

A : B = 3 : 7  (Efficiencies)

⇒ Total work = (3 + 7) x 14 = 10 x 14 = 140 units,   ..(Efficiency × Days = Total work)

⇒ B worked for 8 days alone and left the work = 7 x 8 = 56 units,

⇒ Remaining work = 140 - 56 = 84 units,

⇒ Time required for to complete the work alone = \(\frac{84}{3}\) = 28 days,      ..(\(\frac{Work}{Efficiency}\) = Time)