FIND :
A group of workers was put on a job. From second day onwards two workers were
withdrawn each day. The job was finished when only two workers worked on the last
day. Had no worker been withdrawn at any stage, the group would have finished the
job in 55% of the time. How many workers were there in the group ? (Each worker
does the same amount of work each day)
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Answer:
Assuming n is the number of workers:
On day 1 they will produce n units of work.
On day 2 they will produce n-1 units of work
[..]
On day n they will produce 1 unit of work (and finish the job in n days)
The total amount of work produced is a sum of k with k = 1 to n. This is equal to n(n+1)/2
If no workers are removed. The production will be n units per day (constant).
It will take n(n+1)/2n days to finish and we know this will be equal to 55% of the previous time (which is n)
Hence we have: n(n+1)/2n = 55n/100
Which simplifies to 100n + 100 = 110n
Hence n = 10
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