150 workers were engaged to finish a piece of work in certain numbers of day for workers job the second day for more worker drop the third day and so on it takes 8 more days to finish the work now find the number of days in which the work was completed
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Answer:
25 days
Step-by-step explanation:
Assume the work is completed in n days right before the workers started dropping.
Since the number of workers drop by 4 every day except for the first day, therefore, the total number of workers who worked till the nth day are = the sum of n terms of an Arithmetic Sequence (since the common difference is always 4). The first term of the A.P. is 150.
Hence, the A.P. is =n(150-2n)
If the workers hadn't dropped, the work would have been finished in (n-8) days with 150 workers working every day.
Therefore, the total number of workers who would have worked the n days = 150(n-8).
Hence,
Therefore, the work was completed in 25 days.
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