150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was complete.

Answer

N/a

Explanation

Let the work is completed in 'n' days.
No. of workers engaged on second day =150-4=146
No. of workers engaged of third day `=150-2xx4=142`
Series formed from n terms : 150, 146, 142,….
Hera `a=150, d=146-150 = 142-146=-4`
`therefore" "S_(n)=(n)/(2)[2a+(n-1)d]`
`=(n)/(2)[2xx150+(n-1)(-4)]=152n-2n^(2)`
If 150 workers engaged then work completes in (n-8) days
`therefore" "150(n-8)=152-2n^(2)`
`rArr" "2n^(2)-2n-1200=0`
`rArr" "n^(2)-n-600=0`
`rArr" "(n-25)(n+24)=0`
`rArr" "n-25=0 or n+24=0`
`rArr" "n=25 or" "n=-24`
`n=-24` is not possible.
Therefore, work is completed in 25 days.