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 From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-thirds the time.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?
Explanation:
Let efficiency of each worker by 1 unit/day.
Case 1: When a worked leaves every day.
Since n workers start on day 1 and on last day only 1 worker will remain, hence, the work will last n days.
⇒ Total work done = n × 1 + (n - 1) × 1 + (n - 2) × 1 + … + n × 1 = n(n+1)/2 …(1)
Case 2: When no workers leave
Time taken is 2/3rd of n days.
⇒ Total work done = n × 2/3 n = 2/3 × n2 …(2)
Since same work is done in both the cases, we can equate (1) and (2).
n(n + 1)/2 = 2/3 × n2
⇒ n = 3.
Hence, option (b).
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