Question

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 third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

Answer 1

150 workers complete the work in n days

1 day work of 150 employees = `1/"n"`

1 day work of 1 employee = `1/(150"n")`

On the first day, 150 workers do `150/(150"n")` work in 1 day.

On the second day 146 workers do `146/(150"n")` work in 1 day.

On the third day 142 workers do `146/(150"n")` work in 1 day.

That work was completed in n + 8 days

∴ `150/(150"n") + 146/(150"n") + 142/(150"n") + ...... ("n" + 8 )` terms = 1

or `1/(150"n")[150 + 146 + 142 + .... ("n" + 8)  "terms"] = 1`

or `("n" + 8)/(2(150"n")) [2 xx 150 + ("n" + 8 -1) xx (-4)] = 1`

(n + 8) [300 – 4(n + 7)] = 300n

or (n + 8) (−4n + 272) = 300n

or (n + 8) (n – 68) = –75n

or n2 – 60n – 544 = –75n

or n2 + 15n – 544 = 0

or (n + 32) (n – 17) = 0

n ≠ –32 or n = 17

Total time = n + 8 days

= 17 + 8

= 25 days