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150 workers can do a work in n day from second day 4 workers started leaving on each day so work completes in 8 more days find no of days to complete it?
Wiki User
∙ 14y ago
150 workers-- n days-- 'x' amount of work is done by 150 workers in 'n' days
1 worker-- 1 day-- 'x/(150n)' amount of work done by 1 worker in 1 day
Let's calculate the amount of work done by the reducing number of workers in n+8 days:
Work on first day= Number of workers on first day * amount of work done by 1 worker in 1 day.
= 150 * [x/(150n)]
Work on second day= Number of workers on second day * amount of work done by 1 worker in 1 day.
= 146 * [x/(150n)]
Work on (n+8)th day= Number of workers on (n+8)th day * amount of work done by 1 worker in 1 day.
= [150+(n+8-1)(-4)] * [x/(150n)] --using arithmetic sequence formula
= [122-4n] * [x/(150n)]
Total work=[(n+8)/2 * (150 + 122-4n )] * [x/(150n)] --using sum of arithmetic sequence formula
= [120n-2n2+1088] * [x/(150n)]
x amount of work can be done in n days
[120n-2n2+1088] * [x/(150n)] amount of work is done in n+8 days
x/n= [ (120n-2n2+1088 )* x/(150n) ] / (n+8)
Solving this, we get:
n2+15n+56=0
n= -8, -7
Since the days are obtained in negative, I assume there is something wrong with the data in the question.
Wiki User
∙ 14y ago
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