Time Work

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-thirds the time. How many workers were there in the group?

  1. 2
  2. 3
  3. 5
  4. 11

Answer

Let there were n workers on a job.

Since job was finished when last worker was withdrawn, time taken = n days

Let 1 unit of work is done by one worker in one day. 

Work done on 1st day = n*1 = n

Work done on 2nd day = (n-1)*1 = n-1

n + (n-1) + ... + 2 + 1 = n*2n/3 = 2n2/3

n(n+1)/2 = 2n2/3

3n + 3 = 4n

n = 3

The correct option is B.