Question

150 workers were engaged to finish a work in a certain number of days for workers dropped on the 2nd day and 4 more workers dropped on the third day and so on it takes 8 more days to finish the work now find the number of days in which the workers have concluded

Answer 1

Sol: Suppose the work is completed in n days.            

Since 4 workers went away on every day except the first day.

∴ Total number of worker who worked all the n days is the sum of n terms of A.P. with first term 150 and common difference – 4.

Total number of worker who worked all the n days = n/2[2 x 150 + (n-1) x -4 ] =  n (152 – 2n)

If the workers would not have went away, then the work would have finished in (n – 8) days with 150 workers working on every day.

∴ Total number of workers who would have worked all n days = 150 (n – 8)

∴ n (152 – 2n) = 150 (n – 8)  ⇒ 152n – 2n2 = 150n – 1200      ⇒ 2n2 – 2n – 1200 = 0

⇒ n2 – n – 600 = 0                 ⇒ n2 – 25n + 24n – 600 = 0        ⇒ n(n – 25) + 24 (n + 25) = 0

⇒ (n – 25) (n + 24) = 0 ⇒ n – 25 = 0 or n + 24 = 0                 ⇒ n = 25 or n = – 24

⇒ n = 25 ( Number of days cannot be negative)

Thus, the work is completed in 25 days.