Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and 75 days. They started the work together but Nikhil left after 5 days of start and Somesh left 2 days before the completion of the work. In how many days will the work be completed?

Let the duration in which the will be completed be 't' days.

The portion of work done by Nikhil = $$\frac{5}{75}$$= $$\frac{1}{15}$$                    ( Since He worked for 5 days)

Somesh left 2 days early that means Somesh must have worked for 't-2' days

The portion of work done by Somesh = (t-2)*$$\frac{1}{45}$$

Similarly, the portion of work  done by Tarun = t*$$\frac{1}{60}$$

Solving for t

          $$\frac{1}{15}$$+(t-2)*$$\frac{1}{45}$$+t*$$\frac{1}{60}$$ = 1

             $$\frac{4(t-2)+3t}{180}$$   = $$\frac{14}{15}$$

                      t=$$25\frac{1}{7}$$

Therefore, option A is the correct answer.