PS:Work problem

[cesar.rodriguez.blanco]

I do not how to solve this problem.
Source: Beatthegmat.

Edusoft, a software firm has engaged certain number of men to finish a project in the stipulated time. But after working for 14 days, 1/4 of them have left and to complete the remaining project the remaining members have taken as many days as the initial number of men would have taken to complete the entire project. In how many days was the project completed?

A. 48 B. 60 C. 56 D. 40 E. None of these

[kevinmarmstrong]

Suppose that with the n men who started, the task would be done in d days. Thus the task requires nd men-days.

After 14 days (d-14)n men-days of work remains, which will be done in d days by the 3n/4 men still on the job.

Thus n(d-14) =3nd/4 and d=56. Thus the project was completed in 14 + 56 = 70 days

You could also reason that 3/4 of the workforce would, in the time it takes the entire workforce to do the job, do 3/4 of the job. Thus 1/4 of the job was done in the first 14 days and consequently the entire job could be done by the entire workforce in 56 days. 14 + 56 = 70

[Ben Ku]

I like Kevin's response. Let me know if it's unclear or if you have additional questions. Thanks.