Math, asked by sakshamlok, 1 year ago

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

Answers

Answered by paulaiskander2
5

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,

n(150-2n) = 150(n-8)\\152n-2n62=150n-1200\\2n^2-2n-1200=0\\n^2-n-600=0\\(n-25)(n+24)=0\\n=25

Therefore, the work was completed in 25 days.

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