A started a work and left after working for 8 days. B finished the remaining work in 14 days. If A left the work after working 9 days then B would have finished the remaining work in 10 days. In how many days they can finish the whole work working together?

9\(\frac{1}{5}\)

ATQ, If A works for 1 extra day then B finish the work 4 days earlier.

1 day of A's work = 4 days of B's work

Efficiency ratio = A : B = 4 : 1

Total work = No. of days × efficiency

                 =  (9 x 4) + (1 x 10) = 46              (according to 2nd condition)

A & B together finish the work in = \(\frac{46}{5}\) = 9\(\frac{1}{5}\)