A group of workers was put on a job. From the second day onwards, 1 worker left work everyday. If no worker was left when 52% of the work gets completed, find the number of workers in the group initially?
Let x men doing a work and from second day onwards 1 worker left work, then wok will be completed in x days. x + x – 1 + x – 2 + ……….. x – n = x men Sum of n numbers(Sn) = n/2 [2a + (n -1)d] ⇒ x/2 [2 x + (x -1)(-1)] ⇒ x/2 [2 x – x + 1] ⇒ x/2 [x + 1] If no one would leave the work then, x/2 [x + 1] = x × x × 52/100 ⇒ x + 1 = 52x/50 ⇒ 50x + 50 = 52 x ∴x = 25
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