Question

A group of workers can complete a certain job in 9 days. But it so happens that every alternate day starting from the second day, 2
workers are withdrawn from the job and every alternate day starting from the third day, one worker is added to the group. In such a
way, the job is finished by the time there is no worker left. If it takes the double time to finish the job now, find the number of
workers who started the job?​

Answer 1

Let the number of workers be X.

Then, the total work = 9X man days.

As per the given condition, number of workers starting with the first day will be X, X - 2, X - 1, X - 3, X - 2, X - 4, X - 3… and so on till 18 days. So separating the odd and even terms and adding (9X - 36) + (9X - 54) = 9X

=> X = 10