Question:
a contractor employed 150 workers to complete a certain job in anumber of days. due to partly wages every 4 days 4 worker start dropping.it took 8 more days to complete the work.in how may days the job was completed
Answer:
Let the job was completed in n days.
Total number of employes = 150
Let 150 employees take (n - 8) days to complete the work.
So, total workdone = 150(n - 8)
Given that every day, 4 worker start dropping.
Now, the first day, number of employees = 150
2nd day, number of employees = 150 - 4 = 146
3rd day, number of employees = 146 - 4 = 142
and so on.
So, 150 + 146 + 142 + ...........up to n terms = 150(n - 8)
=> (n/2)*{2*150 + (n - 1)*(-4)} = 150(n - 8)
=> n*{150 + (n - 1)*(-2)} = 150(n - 8)
=> n*{150 - 2n + 2} = 150(n - 8)
=> n*{152 - 2n} = 150(n - 8)
=> 152n - 2n2 = 150n - 1200
=> 2n2 + 150n - 1200 - 152n = 0
=> 2n2 - 2n - 1200 = 0
=> n2 - n - 600 = 0
=> (n - 25)*(n + 24) = 0
=> n = 25, -24
Since n can not be negative,
So, n = 25
Hence, it takes 25 days to complete the work.
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