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?

To do a certain work, the ratio of efficiencies of A and B is 3 : 7.

Let's assume the efficiencies of A and B are 3y and 7y respectively.

Working together, they can complete a work in 14 days.

Total work = $$14\times(3y+7y)$$ = $$14\times10y$$ = 140y

B started the work and after working for 8 days, he left and A completed the remaining work.

Let's assume the number of days A worked is 'd'.

$$7y\times8 + 3y\times d = 140y$$

$$7\times8 + 3\times d = 140$$

56 + 3d = 140

3d = 140-56 = 84

number of days A worked = d = 28 days